CTP Content Standards Manual

If you have any questions, please contact ERB Support at (866) 683-2335 or (646) 503-2699 or send an e-mail to [email protected]. Copyright 2014 Educational Records Bureau DEAR ERB MEMBER SCHOOL Welcome to the CTP Content Standards Manual. If you are reading this, you are most likely one of the many ERB member schools that use the CTP, ERB’s Comprehensive Testing Program, and are interested in learning more about our standards and this assessment.

ERB, a non-profit educational institution founded in 1927, was built on quality achievement assessments and high standards. ERB’s tests provide rigorous, level-appropriate assessments of student progress in meeting these essential academic standards. And now, we’re taking our commitment even further, making all of our assessments available online for instant, actionable results. CTP is no exception and is now available in the traditional paper-pencil version (CTP 4) and an online version (CTP Online).

Whether you are administering the CTP online, or using our CTP4 paper and pencil version, you will find that this guidebook will be a valuable and useful resource. It is designed to help you, and your faculty, understand both the standards that are the foundation of the CTP assessment, and the types of items that students address when taking the CTP. It is also a useful tool to have on hand when conferencing with parents as to their child’s results.

This Content Standards Manual (CSM) has two sections. The first section outlines the standards by level and provides references to related sample test items. The second section holds sample items for each subtest and level, so you can see how the item is formatted and appears to the student. In combination, the CSM allows you to see what the student is being asked, and how it may be asked, by giving you item samples associated with that standard across all levels.

We hope that you will find this to be a very useful and valuable tool. It will certainly assist you and others as you analyze the data offered through our many CTP reports and reflect on your curriculum in the year ahead!

WITH WARM REGARDS The ERB Staff

COPYRIGHT © 2014 | ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED OR REDISTRIBUTED 2 | CTP CONTENT STANDARDS MANUAL WITHOUT PERMISSION. CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] 470 PARK AVENUE SOUTH, SECOND FLOOR SOUTH TOWER, NEW YORK, NEW YORK 10016 TABLE OF CONTENTS

INTRODUCTION SUPPORT & CONTACTS WHAT IS CTP?...... 4 ERB offers on-going assistance to its CTP users throughout the HOW DO I USE THE CTP CONTENT STANDARDS entire testing process! MANUAL?...... 4 WHAT ARE THE CTP COMPONENT TESTS?...... 5 The CTP Portal Help and Resources Page The CTP Portal is your one-stop-shop for all things CTP! Video tutorials, manuals, and other charts and guides can be found SCOPE AND SEQUENCE here that will answer a variety of testing questions. VERBAL TESTS...... 6 MATHEMATICS TESTS...... 7 CTP Operations For assistance with using the CTP Portal please call CTP Operations at (866)-683-2335 or (646) 503-2699 CONTENT CATEGORIES or email [email protected]. LEVEL 1...... 8 ERB Academic Professionals Verbal Subtests...... 8 For assistance with reports, scheduling, or suggestions for Mathematics Subtests...... 9 distribution of reports, please contact the ERB Academic LEVEL 2...... 10 Professional in your region by visiting www.erblearn.org/schoolsupport. Verbal Subtests...... 1 0 Mathematics Subtests...... 12 LEVEL 3...... 13 Presentations, Workshops, and Conferences ERB offers presentations to inform schools about ERB’s Verbal Subtests...... 13 Mathematics Subtest...... 15 products and services. ERB also offers workshops in person or online to help teachers and administrators analyze and LEVEL 4...... 17 interpret test results. Presenters and workshop leaders are ERB Verbal Subtests...... 17 staff members and specially trained consultants. The content Mathematics Subtests...... 19 and length of presentations and workshops are tailored to the LEVEL 5...... 21 needs of the particular group or audience. ERB also provides Verbal Subtests...... 21 mini-workshops for special groups, such as parents and boards Mathematics Subtests...... 2 3 of education. Additionally, every year in the late fall ERB hosts LEVEL 6...... 25 an informative and exciting member conference that our schools find very worthwhile. For more information on Verbal Subtests...... 2 5 workshops, please call ERB at (800)-989-3721 or visit Mathematics Subtests...... 2 7 www.erblearn.org/schoolsupport to contact the ERB LEVEL 7...... 29 Academic Professional in your region. Verbal Subtests...... 29 Mathematics Subtests...... 31 LEVEL 8...... 33 Verbal Subtests...... 33 Mathematics Subtests...... 35 LEVEL 9...... 38 Verbal Subtests...... 38 Mathematics Subtests...... 40 LEVEL 10...... 43 Verbal Subtests...... 43 Mathematics Subtests...... 45

SAMPLE QUESTIONS LEVELS 1-2...... 47 LEVEL 3...... 54 LEVELS 4-6...... 63 LEVELS 7-10...... 76

3 | CTP CONTENT STANDARDS MANUAL INTRODUCTION

WHAT IS CTP? What types of questions are on the CTP? CTP tests whether administered online, or paper /pencil, are composed The Comprehensive Testing Program (CTP) is a rigorous of multiple choice questions. There is an optional constructed- assessment of individual student and group achievement of response (open ended) section on the CTP 4, requiring essential standards and learning domains in English language students to write short answers. In addition, CTP Online offers arts and mathematics. All CTP subject subtests were developed schools the ability to test students in Science for Levels 3 and by Educational Testing Services (ETS) and ERB to align with up. The Reasoning sections (Levels 3 and up) are Verbal the National Council of Teachers of English, International Reasoning and Quantitative Reasoning. The Achievement Reading Association and the National Council of Teachers of sections complement this vital information through a series of Mathematics Principles and Standards. In addition, in review English Language Arts Achievement Subtests and Mathematics of the Common Core Standards, CTP has strong alignment, Subtests. Comparisons between Reasoning results and having been a rigorous and well developed assessment based Achievement results are unique to the CTP and very valuable on these standards from its inception well before the Common data to consider. Core.

The CTP provides useful information about student performance in grades 1-11 in listening, reading, vocabulary, HOW DO I USE THE CTP writing, mathematics, and science*. In addition, CTP assesses CONTENT STANDARDS MANUAL? verbal and quantitative reasoning skills and abilities in Levels With reports in hand, or to answer questions that you may have 3–11. The combined measures can be used to compare more on our standards, we suggest that you find the test level or the content-specific, curriculum-based indicators of performance standard you wish to explore and then review the associated (scores on the achievement tests) to the more conceptual items that may help you understand how the student was asked knowledge base that helps to gauge potential and support to show their understanding of the concepts. school achievement (scores on the reasoning tests). This comparison can prove highly useful, especially for students whose reasoning and achievement scores exhibit marked Scope and Sequence The Scope and Sequence chart discrepancies. In addition, the CTP offers schools the ability to provides an overview of the general content areas tested at offer testing accommodations as needed. each level of the CTP.

*CTP Online only Content Categories As mentioned above, this manual documents the developmentally appropriate standard as What information does CTP provide to guide outlined and addressed in each subtest in each domain by instruction and chart student growth? Our score level. The standards are presented in sequence and associated reports are powerful tools helping to guide learning decisions sample items are highlighted in each area/level. Descriptions on both an individual and group level. For faster, more provide more detailed information about the concepts and efficient reporting, all CTP 4 and CTP Online reports are now skills tested at each level. At most levels, specific skills are available through our CTP portal. There are many types of CTP linked to sample questions that appear later in the book; the reports in a variety of formats; individual, group, roster and relevant sample questions are indicated by bold, orange text customizable data downloads. All CTP score reports provide e.g. Reading Comprehension Sample Question 1. robust information on the student, class, and school level to help inform teaching and learning, and enable next step Sample Questions and Explanations The sample instruction. Comparative information (national, suburban questions are intended to provide a general idea of the kinds of public, independent school, and association norm groups, as questions that will appear on the CTP. The questions in this well as local/school norms) is always available. Reports can be book were all administered operationally in pilot tests and also be customized on the portal by the school to illuminate represent a cross section of the content areas and skills class level or group level data. Data is held for three years on assessed in operational tests. The questions are clustered into the CTP Portal allowing your school to access reports over groups by level, and each question is followed by an time. Growth reports become available in year two of testing. explanation of the correct answer and an indication of the Parent reports are also among the report options available to content category exemplified by the question. schools.

When can I administer the CTP? The CTP is a diagnostic instructional tool that works best when administered in the natural flow of the school year. There are two testing windows (fall and spring). We consider the CTP to be a low stakes test that is designed to assist teaching and learning. As such, we recommend that you consider how and when you need the data and offer the test in a season that fits your schedule.

4 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] INTRODUCTION

WHAT ARE THE CTP Mathematics Tests COMPONENT TESTS? The CTP Mathematics subtests consist of Mathematics, Quantitative Reasoning, and an Algebra I test at the appropriate level. Constructed-response is also available. Verbal Tests Each subtest includes questions that assess students’ The CTP Verbal tests emphasize the development of reading understanding and application of a variety of content and and language skills necessary for effective communication process areas in mathematics. The CTP Mathematics tests both in academic settings and in the world beyond the parallel the NCTM’s categories, with slight modifications that classroom. The CTP Verbal Test assesses students in the are appropriate for each grade level. Students are presented following areas: Word Analysis, Auditory Comprehension, items in mathematics content areas important for students in Verbal Reasoning, Vocabulary, Reading Comprehension, grades K through 12 grouped under five main categories: Writing Mechanics, and Writing Concepts and Skills. Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. CTP Mathematics content Each of these seven subtests represents a distinct facet of areas should be viewed as complementary rather than verbal ability, but the skills measured are interrelated, and the exclusive. tests should be considered parts of a whole and compared to each other as well as to comparative norm groups. Verbal The CTP questions also assess the following mathematical Reasoning assesses the student’s ability to conceptualize processes: Conceptual Understanding, Procedural Knowledge, relationships among words and concepts and draw conclusions and Problem Solving. Questions that are classified under based on incomplete information reasoning analytically, Conceptual Understanding ask students to recognize and categorically, and logically. Vocabulary addresses the notion manipulate fundamental ideas in mathematics. Questions that that reading fluency depends upon an extensive vocabulary are classified under Procedural Knowledge ask students to and the ability to use words appropriately given the context recall factual information about mathematics or to and to distinguish meaning. Reading comprehension demonstrate understanding of basic algorithms. Questions measures a student’s ability to comprehend, evaluate and draw that are classified under Problem Solving ask students to apply conclusions using a variety of strategies to analyze both fiction and integrate concepts or to identify appropriate strategies. and nonfiction text. Levels 3 to 10 of the CTP include Quantitative Reasoning tests The verbal skills and concepts tested in each subtest at each to assess students’ ability to engage in age-level appropriate level build on one another as well as on skills already ways, in pattern recognition, classification, and reasoning in mastered. At Levels 1 and 2, for example, the Word Analysis all content areas, including logic, arithmetic, algebra, tests specifically emphasize the phonemic awareness and geometry, probability, and statistics. In the test questions, decoding skills that are vital for beginning readers. As students must use mathematics to make comparisons, students move through the years, these skills are measured formulate extensions or generalizations of mathematical using developmentally appropriate, but also challenging and concepts, and analyze mathematical situations. complex texts, that assume students will draw upon strategies and skills with increasing fluency and comprehension over For levels 5 through 10 of the CTP Mathematics Tests, time. calculators are allowed on one section of the multiple-choice achievement tests. In the NCTM Standards, the responsible The CTP Writing Mechanics subtest asks students to identify use of calculators is encouraged. Technology is said to “aid in misspellings, recognize and correct mistakes in capitalization, assessment,” by allowing an alternate means to examine and punctuation. The Writing Concepts and Skills subtest students’ processes. However, the NCTM Standards also state integrates a student’s growing facility with grammar and that “technology should not be used as a replacement for basic usage, their understanding of and recognition of the essential understandings and intuitions.” The CTP tests therefore do not elements/traits outlined in the writing process through an allow the use of calculators on any of the following tests: the analysis of sentences presented. Overall, the Verbal tests offer a constructed-response component of the achievement tests, the rich lens with which to view a student’s achievement and Quantitative Reasoning tests, and the Algebra I test. This reasoning skills in English Language Arts. statement does not in any way diminish the benefits of CTP Online, which follows the same guidelines and standards, however, uses technology to enhance the testing experience, thereby engaging the modern student.

5 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] SCOPE AND SEQUENCE: VERBAL TESTS

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 Spring to Fall Grades: 1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to 11

Word Analysis Sight Words Phonic Analysis Structural Analysis Auditory Comprehension Vocabulary in Context Explicit Information Inference Analysis Reading Comprehension Vocabulary in Context Explicit Information Inference Analysis Reading for Understanding (optional CTP 4 only constructed-response section) Writing Mechanics Spelling Capitalization Punctuation Usage Spelling, Capitalization, and Punctuation (combined) Sentence Construction Writing Concepts and Skills Organization Purpose, Audience, and Focus Supporting Details Style and Craft Verbal Reasoning Analogical Reasoning Categorical Reasoning Logical Reasoning Vocabulary Word Meanings Precision Application

6 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] SCOPE AND SEQUENCE: MATHEMATICS TESTS

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 Spring to Fall Grades: 1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to 11

Mathematics Number Sense and Operations with Whole Numbers Number Sense and Operations with Fractions and Decimals Number Systems and Number Theory Number and Number Relationships Geometry and Spatial Sense Measurement Probability Statistics Pre-Algebra Data Analysis, Statistics, and Probability Patterns, Functions, and Pre-Algebra Algebra Functions Conceptual Understanding Procedural Knowledge Problem Solving Math Communication (optional CTP 4 only constructed-response section) Quantitative Reasoning Comparison Extensions/Generalizations Analysis Algebra 1 Expressions, Statements, and Matrices Equations and Inequalities Tables, Graphs, and Algebraic Geometry Situations Involving Variable Quantities

7 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 1 Sample Questions on pages 47-53

AUDITORY COMPREHENSION Vocabulary in Context The student will be able to use context clues to determine the The CTP Auditory Comprehension test at Level 1 measures meaning of a word or phrase in a text and choose the correct students’ ability to understand and interpret information definition or synonym. Levels 1-2 Sample Question 3 presented orally. In addition to being able to listen to and follow the directions for taking the test itself, students must Explicit Information also be able to recognize and understand important words and The student will be able to identify explicit details from a plot points and to interpret and analyze information presented passage and provide answers to “who,” “what,” “where,” “when,” in a story read aloud. The development of good listening skills “why,” and “how” questions about the text. parallels and reinforces the development of good reading skills, and the skills tested in the Auditory Comprehension test Inference therefore parallel those tested in the Reading Comprehension The student will be able to: test. The following is a list of the skills measured by the CTP • Use implicit information from a passage to make inferences Auditory Comprehension test at Level 1. about the motives or behaviors of characters. • Use implicit information from a passage to summarize or Vocabulary in Context draw conclusions. Levels 1-2 Sample Questions 4 & 6 The student will be able to use context clues to determine the meaning of a word or phrase in a text read aloud and choose Analysis the correct definition or synonym. The student will be able to: Explicit Information • Draw connections between and among various pieces of The student will be able to identify explicit details from a information in a text. Levels 1-2 Sample Question 7 passage read aloud and provide answers to “who,”“what,” • Synthesize explicit and implicit information to make “where,”“when,”“why,” and “how” questions about the text. predictions or draw conclusions about a text. Levels 1-2 Levels 1-2 Sample Questions 1 & 2 Sample Question 5

Inference The student will be able to: Reading for Understanding • Use implicit information from a passage read aloud to make Optional Constructed-Response Section* inferences about the motives or behaviors of characters. Students use their developing productive language skills to • Use implicit information from a passage read aloud to answer questions about text, employing comprehension summarize or draw conclusions. strategies to interpret and analyze the texts, describe important aspects of the texts, synthesize information from two texts, and Analysis compare and contrast elements within a text and/or between The student will be able to: two texts. At level 1, most of the questions focus on information that is explicitly stated in the passages. The student will be able • Draw connections between and among various pieces of to: information in a text read aloud. • Describe the main idea of a passage. • Synthesize explicit and implicit information to make predictions or draw conclusions about a text read aloud. • Describe a supporting idea in a passage. Levels 1-2 Sample Question 8 READING COMPREHENSION • Compare and contrast elements from two texts. Levels 1-2 Sample Question 9 The CTP Reading Comprehension test at Level 1 measures • Synthesize information from two texts to make predictions or students’ ability to understand and interpret written text. The draw conclusions NCTE/IRA Standards for the English Language Arts emphasizes the importance of being able to use a “wide range of strategies NOTE: Although the Reading for Understanding section to comprehend, interpret, evaluate, and appreciate text,” does require students to write their answers, it is a test of including “word identification strategies” (31). The CTP reading comprehension and not writing ability. Students’ Reading Comprehension test requires students to draw on responses are evaluated based on how completely and thoroughly they answer the questions; misspellings, these strategies to interpret and analyze a range of texts, both grammatical mistakes, and other writing errors do not fiction and nonfiction. The following is a list of the skills count against them. The questions are scored on a 0-2 measured by the CTP Reading Comprehension test at Level 1. scale.

* Available for CTP 4 only.

8 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 1 Sample Questions on pages 47-53

WORD ANALYSIS • Understand the properties of arithmetic operations, including operations with zero, understand even and odd Systematic vocabulary development is essential for reading numbers, and multiply by multiples of 10. fluency, and building phonemic awareness — learning the • Solve real-life problems involving number operations, sound structure of language — is important for students in including basic money problems. Levels 1-2 Sample grades 1-3. Students must be able not only to recognize Question 15 familiar words but to decode unfamiliar ones. The CTP Word Analysis test at Level 1 measures students’ ability to recognize Geometry and Spatial Sense and decode words. In addition, the test measures The student will be able to: understanding of basic structural elements of the English • Identify basic geometric figures and describe shapes, language, including morphemes and root/base words. The including circles, triangles, and rectangles. Levels 1-2 following is a list of the skills measured by the CTP Word Sample Question 16 Analysis test at Level 1. • Understand basic properties of figures, including closure, Sight Words number of sides, vertices, and angles, and characterize lines The student will be able to recognize common words that are as intersecting or parallel. Levels 1-2 Sample Question 17 vital to reading fluency, especially those that do not follow • Identify relationships between figures and images under basic rules of sound- letter correspondence. transformations; identify lines of symmetry and the effects of combining, subdividing, and changing basic shapes; and Phonemic Analysis graph coordinates on a map grid. The student will be able to recognize vowel and consonant sounds and blends in varying positions within a word (initial, Measurement medial, and final). The student will be able to:

Structural Analysis • Know the approximate sizes of customary and metric units The student will be able to: and the relationships between measures within the same system and select appropriate units of measure • Recognize compound words. Levels 1-2 Sample Question 10 • Work with the basic measure of perimeter and area • Understand the correct use of contractions and what they mean. • Solve real-life problems involving coins, elapsed time, calendars, temperature, weight, or distance and read time • Choose the root/base word with the appropriate inflectional on a standard clock and degrees on a thermometer ending in the context of a sentence. Data Analysis, Statistics, and Probability MATHEMATICS The student will be able to read and interpret various types of simple graphs, including bar, line, circle, pictorial graphs, and The five content strands in the Level 1 Mathematics tests are: 1) tables and tallies. Numbers and Operations with Whole Numbers; 2) Geometry and Spatial Sense; 3) Measurement; 4) Data Analysis, Statistics, Patterns, Functions, and Pre-Algebra and Probability; and 5) Patterns, Functions, and Pre-Algebra. The student will be able to: Along with subscores in the content areas, students receive • Recognize a wide variety of patterns and the rules that subscores in three process areas: Conceptual Understanding, explain them. Procedural Knowledge, and Problem Solving. In addition, students receive a subscore in Mathematics Communication if • Select number sentences to represent problem situations. they take the constructed-response component of the Levels 1-2 Sample Question 18 achievement test (available for CTP 4 only). The following is a list of the skills measured by the CTP Mathematics Math Communication Achievement test at Level 1. Optional Constructed-Response Section* The constructed-response component of the Achievement tests Number Sense and Operations with Whole Numbers assesses students’ ability to communicate in mathematics. At The student will be able to: this level, the work students will be able to do includes: • Use place value, read, write, and compare whole numbers, completing charts, making graphs, writing number sentences, use models to represent numbers, and use expanded understanding monetary units represented by coins, notation. extending patterns, and constructing geometric figures to represent problems. Levels 1-2 Sample Questions 19 & 20 • Add and subtract whole numbers, multiply single-digit numbers, know the language of basic operations, * Available for CTP 4 only understand the relationship between addition and multiplication, and estimate sums, differences, products, and quotients.

9 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 2 Sample Questions on pages 47-53

AUDITORY COMPREHENSION Explicit Information The student will be able to: The CTP Auditory Comprehension test at Level 2 measures • Use explicit information to identify the main idea or primary students’ ability to understand and interpret information purpose of a text or part of a text. presented orally. In addition to being able to listen to and • Identify explicit details from a passage and provide answers follow the directions for taking the test itself, students must to “who,” “what,”“where,”“when,”“why,” and “how” also be able to recognize and understand important words and questions about the text. plot points and to interpret and analyze information presented in a story read aloud. The development of good listening skills Inference parallels and reinforces the development of good reading The student will be able to: skills, and the skills tested in the Auditory Comprehension test therefore parallel those tested in the Reading Comprehension • Use implicit information from a passage to make inferences test. The following is a list of the skills measured by the CTP about the motives or behaviors of characters. Auditory Comprehension test at Level 2. • Use implicit information from a passage to summarize or draw conclusions. Vocabulary in Context The student will be able to use context clues to determine the Analysis meaning of a word or phrase in a text read aloud and choose The student will be able to: the correct definition or synonym. • Draw connections between and among various pieces of Explicit Information information in a text. The student will be able to identify explicit details from a • Synthesize explicit and implicit information to make passage read aloud and provide answers to “who,”“what,” predictions or draw conclusions about a text. “where,”“when,”“why,” and “how” questions about the text. Reading for Understanding Inference Optional Constructed-Response Section* The student will be able to: Students use their developing productive language skills to • Use implicit information from a passage read aloud to make answer questions about text, employing comprehension inferences about the motives or behaviors of characters. strategies to interpret and analyze the texts, describe • Use implicit information from a passage read aloud to important aspects of the texts, synthesize information from summarize or draw conclusions. two texts, and compare and contrast elements within a text and/or between two texts. At level 2, most of the questions Analysis focus on information that is explicitly stated in the passages. The student will be able to: The student will be able to: • Draw connections between and among various pieces of • Describe the main idea of a passage. information in a text read aloud. • Describe a supporting idea in a passage. • Synthesize explicit and implicit information to make • Compare and contrast elements from two texts. predictions or draw conclusions about a text read aloud. • Synthesize information from two texts to make predictions READING COMPREHENSION or draw conclusions. NOTE: Although the Reading for Understanding section The CTP Reading Comprehension test at Level 2 measures does require students to write their answers, it is a test of students’ ability to understand and interpret written text. The reading comprehension and not writing ability. Students’ NCTE/IRA Standards for the English Language Arts emphasizes responses are evaluated based on how completely and the importance of being able to use a “wide range of strategies thoroughly they answer the questions; misspellings, to comprehend, interpret, evaluate, and appreciate text,” grammatical mistakes, and other writing errors do not including “word identification strategies” (31). The CTP count against them. The questions are scored on a 0-2 scale. Reading Comprehension test requires students to draw on these strategies to interpret and analyze a range of texts, both * Available for CTP 4 only. fiction and nonfiction. The following is a list of the skills measured by the CTP Reading Comprehension test at Level 2.

Vocabulary in Context The student will be able to use context clues to determine the meaning of a word or phrase in a text and choose the correct definition or synonym.

10 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 2 Sample Questions on pages 47-53

WORD ANALYSIS WRITING MECHANICS Systematic vocabulary development is essential for reading The development of a foundational understanding of language fluency, and building phonemic awareness — learning the conventions and mechanics is essential as students move from sound structure of language — is important for students in copying letters and words to writing sentences to composing grades 1-3. Students must be able not only to recognize paragraphs. The NCTE/IRAStandards for the English Language familiar words but to decode unfamiliar ones. The CTP Word Arts indicates that students should be able to “apply knowledge Analysis test at Level 2 measures students’ ability to recognize of language structure and language conventions (e.g., spelling and decode words and to choose words appropriate for the and punctuation) . . . to create, critique, and discuss print and context of a sentence or passage. In addition, the test measures non-print texts” (36). The CTP Writing Mechanics test at Level 2 students’ increasingly sophisticated understanding of basic measures students’ growing understanding of English structural elements of the English language, including sentence structure and language conventions. The following is morphemes and root/base words and correct plural and a list of the skills measured by the CTP Writing Mechanics test adjectival forms. The following is a list of the skills measured at Level 2. by the CTP Word Analysis test at Level 2. Spelling Sight Words The student will be able to identify misspellings of commonly The student will be able to recognize common words that are used words, including words with affixes and words that vital to reading fluency, especially those that do not follow display improper pluralization. basic rules of sound-letter correspondence. Capitalization Phonemic Analysis The student will be able to recognize correct and incorrect The student will be able to recognize vowel and consonant capitalization. Specific rules tested include: sounds and blends in varying positions within a word (initial, • Capitalization of proper nouns. medial, and final).Levels 1-2 Sample Questions 11 & 12 • Capitalization of the first word of a sentence. Structural Analysis The student will be able to: Punctuation The student will be able to recognize correct and incorrect • Recognize compound words. punctuation. Specific rules tested include: • Understand the correct use of contractions and what they • Proper punctuation for dialogue and letter writing. mean. • Correct end punctuation. • Choose the root/base word with the appropriate inflectional ending in the context of a sentence. • The correct use of the comma. • Choose the correct plural form of a word in context. • The correct use of the apostrophe in contractions and possessives. Levels 1-2 Sample Question 13 • Understand the correct use of comparative and superlative adjectives. Usage • Use context clues to choose the appropriate word to fill in a The student will be able to apply rules of English diction and blank in a sentence. grammar. Specific rules tested include: • Correct pronoun use, including pronoun-antecedent agreement. • Rules of diction within the context of a sentence. • Correct verb form and tense, including subject-verb agreement. Levels 1-2 Sample Question 14

11 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 2 Sample Questions on pages 47-53

MATHEMATICS Measurement The student will be able to: The five content strands in the Level 2 Mathematics tests are: • Know the approximate sizes of customary and metric units 1) Numbers and Operations with Whole Numbers; 2) Geometry and the relationships between measures within the same and Spatial Sense; 3) Measurement; 4) Data Analysis, Statistics, system and select appropriate units of measure. and Probability; and 5) Patterns, Functions, and Pre-Algebra. • Work with the basic measure of perimeter and area. The content strands for Level 2 are the same as the Level 1 content strands; however, the questions are appropriately more • Solve real-life problems involving coins, elapsed time, challenging. Additionally, Level 2 contains a few more calendars, temperature, weight, or distance, and read time questions on Patterns, Functions, and Pre-Algebra than Level on a standard clock and degrees on a thermometer. 1, and there are topics included in Level 2 that are not included in Level 1. These topics are: Data Analysis, Statistics, and Probability The student will be able to: • Understanding the basic concept of chance. • Read and interpret various types of simple graphs, including • Understanding the basic concept of an equality relationship. bar, line, circle, pictorial, table, and tallies. Along with subscores in the content strands, students will • Understand the concept of chance. receive subscores in three process areas: Conceptual Understanding, Procedural Knowledge, and Problem Solving. Patterns, Functions, and Pre-Algebra In addition, students receive a subscore in Mathematics The student will be able to: Communication if they take the constructed-response • Recognize a wide variety of patterns and the rules that component of the achievement test (available for CTP 4 only). explain them. The following is a list of the skills measured by the CTP Sample Questions on page 54 Mathematics Achievement test at Level 2. • Select number sentences to represent problem situations. • Understand the concept of equality. Number Sense and Operations with Whole Numbers The student will be able to: Math Communication • Use place value, read, write, and compare whole numbers, Optional Constructed-Response Section* use models to represent numbers, and use expanded The constructed-response component of the Mathematics test notation. assesses students’ ability to communicate in mathematics. At • Add and subtract whole numbers, multiply single-digit this level, the work students will be able to do includes: listing numbers, know the language of basic operations, mathematically sound results for a problem, naming geometric understand the relationship between addition and shapes, and displaying lines of symmetry. multiplication, and estimate sums, differences, products, * Available for CTP 4 only. and quotients. • Understand the properties of arithmetic operations, including operations with zero, understand even and odd numbers, and multiply by multiples of 10. • Solve real-life problems involving number operations, including basic money problems.

Geometry and Spatial Sense The student will be able to: • Identify basic geometric figures and describe shapes, including circles, triangles, and rectangles. • Understand basic properties of figures, including closure, number of sides, vertices, and angles, and characterize lines as intersecting or parallel. • Identify relationships between figures and images under transformations; identify lines of symmetry and the effects of combining, subdividing, and changing basic shapes; and graph coordinates on a map grid.

12 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 3 Sample Questions on pages 54-62

VERBAL REASONING Explicit Information The student will be able to: The CTP Verbal Reasoning test at Level 3 measures students’ • Use explicit information to identify the main idea or primary ability to conceptualize relationships among words and purpose of a text or part of a text. concepts and to draw conclusions based on incomplete • Identify explicit details from a passage and provide answers information. The ability to infer information that is not to “who,” “what,”“where,”“when,”“why,” and “how” explicitly stated in a text is an essential aspect of fluency in questions about the text. Level 3 Sample Question 4 reading; the CTP Verbal Reasoning test at Level 3 evaluates students’ developing proficiency in this area. The following is a Inference list of the skills measured by the CTP Verbal Reasoning test at The student will be able to: Level 3. • Use implicit information from a passage read aloud to make Analogical Reasoning inferences about the motives or behaviors of characters. The student will be able to: Level 3 Sample Question 5 • Recognize the relationship between two words and identify • Use implicit information from a passage read aloud to another pair of words with the same relationship. Level 3 summarize or draw conclusions. Sample Question 1 Analysis • Identify the definition that accurately describes the The student will be able to: relationship between a pair of words. • Draw connections between and among various pieces of Categorical Reasoning information in a text read aloud. The student will be able to: • Synthesize explicit and implicit information to make • Recognize which of several elements does or does not fit into predictions or draw conclusions about a text read aloud. a thematically grouped list of words. • Generalize about a thematically grouped list of words and choose an appropriate heading for the list. READING COMPREHENSION

The CTP Reading Comprehension test at Level 3 measures Logical Reasoning students’ ability to understand and interpret written text. The The student will be able to: NCTE/IRA Standards for the English Language Arts emphasizes • Solve deductive ordering problems and draw conclusions the importance of being able to use a “wide range of strategies that are directly deducible from the information provided. to comprehend, interpret, evaluate, and appreciate text,” • Solve inductive reasoning problems by reasoning from including “word identification strategies” (31). The CTP details or evidence to a generalization or hypothesis that Reading Comprehension test requires students to draw on makes sense of the evidence. Level 3 Sample Question 2 these strategies to interpret and analyze a range of texts, both fiction and nonfiction. The following is a list of the skills measured by the CTP Reading Comprehension test at Level 3. AUDITORY COMPREHENSION Vocabulary in Context The CTP Auditory Comprehension test at Level 3 measures The student will be able to use context clues to determine the students’ ability to understand and interpret information meaning of a word or phrase in a text and choose the correct presented orally. In addition to being able to listen to and definition or synonym. follow the directions for taking the test itself, students must also be able to recognize and understand important words and Explicit Information plot points and to interpret and analyze information presented The student will be able to: in a story read aloud. The development of good listening skills • Use explicit information to identify the main idea or primary parallels and reinforces the development of good reading purpose of a text or part of a text. Level 3 Sample Question 6 skills, and the skills tested in the Auditory Comprehension test • Identify explicit details from a passage and provide answers therefore parallel those tested in the Reading Comprehension to “who,” “what,”“where,”“when,”“why,” and “how” test. The following is a list of the skills measured by the CTP questions about the text. Level 3 Sample Question 7 Auditory Comprehension test at Level 3.

Vocabulary in Context The student will be able to use context clues to determine the meaning of a word or phrase in a text read aloud and choose the correct definition or synonym.Level 3 Sample Question 3

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READING COMPREHENSION CONTINUED WRITING MECHANICS The development of a foundational understanding of language Inference conventions and mechanics is essential as students move from The student will be able to: copying letters and words to writing sentences to composing paragraphs. The NCTE/IRAStandards for the English Language • Use implicit information from a passage to summarize or Arts indicates that students should be able to “apply knowledge draw conclusions. of language structure and language conventions (e.g., spelling • Use implicit information from a passage to make inferences and punctuation) . . . to create, critique, and discuss print and about the motives or behaviors of characters. Level 3 Sample non-print texts” (36). The CTP Writing Mechanics test at Level 3 Question 8 measures students’ growing understanding of English sentence structure and language conventions. The following is a list of Analysis the skills measured by the CTP Writing Mechanics test at The student will be able to: Level 3. • Draw connections between and among various pieces of information in a text. Spelling The student will be able to identify misspellings of commonly • Synthesize explicit and implicit information to make used words, including words with affixes and words that display predictions or draw conclusions about a text. Level 3 Sample improper pluralization. Question 9 Capitalization Reading for Understanding The student will be able to recognize correct and incorrect Optional Constructed-Response Section* capitalization. Specific rules tested include: Students use their developing productive language skills to • Capitalization of proper nouns. Level 3 Sample Question 12 answer questions about text, employing comprehension strategies to interpret and analyze the texts, describe • Capitalization of the first word of a sentence. important aspects of the texts, synthesize information from • Capitalization in titles and forms of address. two texts, and compare and contrast elements within a text and/or between two texts. At level 3, most of the questions Punctuation focus on information that is explicitly stated in the text. The The student will be able to recognize correct and incorrect student will be able to: punctuation. Specific rules tested include: • Describe the main idea of a passage. • The correct use of the comma. • Describe a supporting idea in a passage. Level 3 • The correct use of the apostrophe in contractions and Sample Question 10 possessives. • Compare and contrast elements from two texts. • Proper punctuation for dialogue and letter writing. • Synthesize information from two texts to make predictions • Correct end punctuation. Level 3 Sample Question 13 or draw conclusions. Level 3 Sample Question 11 Usage NOTE: Although the Reading for Understanding section The student will be able to apply rules of English diction and does require students to write their answers, it is a test of grammar. Specific rules tested include: reading comprehension and not writing ability. Students’ responses are evaluated based on how completely and • Correct pronoun use, including pronoun-antecedent thoroughly they answer the questions; misspellings, agreement. grammatical mistakes, and other writing errors do not • Correct verb form and tense, including subject-verb count against them. The questions are scored on a 0-2 agreement. scale. • Rules of correct and effective expression at the sentence level, *Available for CTP 4 only. including proper modification. • Rules of diction within the context of a sentence. • Rules of sentence boundaries, including avoiding run-ons and fragments.

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WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 3 begins to The Quantitative Reasoning test assesses students’ ability to integrate students’ developing facility with English grammar engage, in age-level appropriate ways, in pattern recognition, and usage with a growing understanding of writing and the classification, and reasoning in all content areas, including writing process. As students begin to develop more logic, arithmetic, algebra, geometry, probability, and statistics comprehensive paragraphs and to learn the stages of the The following is a list of the skills measured by the CTP writing process, the ability to organize complex information Quantitative Reasoning test at Level 3. and to recognize the multiple purposes and audiences for writing becomes increasingly important. According to the Comparison NCTE/IRA Standards for the English Language Arts, it is The student will be able to: important that students be able to “employ a wide range of • Consider numerical quantities in various forms and strategies as they write and use different writing process compare their sizes. Level 3 Sample Question 18 elements appropriately to communicate with different audiences for a variety of purposes” (35). The following is a list • Consider the relative measures of geometric shapes. of the skills measured by the CTP Writing Concepts and Skills • Recognize relative sizes of units of measure, including test at Level 3. between systems.

Organization The student will be able to: Extensions and Generalizations The student will be able to: • Recognize thesis statements, topic sentences, and conclusions. Level 3 Sample Question 14 • Formulate arithmetic conclusions based on observation and mathematical judgment. • Recognize effective transitions between ideas, sentences, and paragraphs. • Formulate geometric conclusions based on observation and mathematical judgment. • Effectively and logically sequence information within a paragraph or passage. • Recognize patterns and geometric representation of real-life situations. Level 3 Sample Question 19 Purpose, Audience, and Focus The student will be able to: Analysis The student will be able to: • Recognize the role of the audience within varying contexts and draw logical conclusions about the intended audience • Interpret symbolic representation of numerical quantities. for a given passage. • Interpret charts, graphs, statistical measures, and basic • Understand how the purpose for and focus of a piece of probability. writing help determine the kind of information included and • Model geometric transformations. the appropriate style and tone of the piece. Level 3 Sample Question 15

Supporting Details The student will be able to: • Choose the appropriate main idea or topic sentence for a paragraph. • Identify effective and relevant details to support a given idea or thesis. Level 3 Sample Question 16

Style and Craft The student will be able to: • Effectively combine two or more sentences into one logical sentence. • Recognize and identify accurate and appropriate word choices in a piece of writing. • Recognize and identify well-crafted sentences that exhibit rhetorical precision. Level 3 Sample Question 17

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MATHEMATICS (PART 1 AND 2) Geometry and Spatial Sense The student will be able to: The six content strands in the Level 3 Mathematics test are: 1) • Use basic geometric language to describe and name shapes, Numbers and Operations with Whole Numbers; 2) Numbers including circles, triangles, and rectangles. and Operations with Fractions and Decimals; 3) Geometry and • Understand basic properties of figures, including number of Spatial Sense; 4) Measurement; 5) Data Analysis, Statistics, sides, vertices, and angles, and characterize lines as and Probability; and 6) Patterns, Functions, and Pre-Algebra. intersecting or parallel. The content strands for Level 3 differ from those for Level 2 in the addition of the strand about fractions and decimals. Even • Identify relationships between figures and images under where the strands are the same, some topics are included in transformation and identify lines of symmetry and the effects Level 3 but not in Level 2. Examples of such topics are: of combining, subdividing, and changing basic shapes. • Using two- and three-dimensional models to represent Measurement whole numbers. The student will be able to: • Dividing whole numbers, including understanding the • Understand approximate sizes in customary and metric units meaning of remainder. and the relationships between measures within the same • Understanding the concepts of mode and range. system. Level 3 Sample Question 23

Along with subscores in the content strands, students will • Use appropriate units of measurement and appropriate tools receive subscores in three process areas: Conceptual for a given measurement and understand basic measure of Understanding, Procedural Knowledge, and Problem Solving. perimeter and area. In addition, students receive a subscore in Mathematics • Solve real-life problems involving coins, elapsed time, Communication if they take the constructed-response calendars, temperature, weight, or distance. component of the achievement test (available for CTP 4 only). The following is a list of the skills measured by the CTP Data Analysis, Statistics, and Probability Mathematics test at Level 3. The student will be able to: Number Sense and Operations with Whole Numbers • Read and interpret various types of simple graphs, including The student will be able to: bar, line, circle, pictorial, tables, and tallies. • Use place value; read, write, and compare whole numbers; • Understand the concepts of mean, mode, and range. use models to represent, order, and compare whole • Understand the concept of chance. numbers; and understand expanded notation.

• Perform arithmetic operations on whole numbers, know the Patterns, Functions, and Pre-Algebra language of basic operations, understand the relationship The student will be able to: between addition and multiplication, and estimate sums, difference, products, and quotients. • Recognize a wide variety of patterns and the rules that explain them. • Understand the properties of arithmetic operations, including operations with zero, understand even and odd • Solve simple open sentences involving operations on whole numbers, and multiply by multiples of 10. Level 3 Sample numbers and select number sentences to represent problem Question 20 situations. • Solve real-life problems involving number operations. Math Communication Optional Constructed-Response Section* Number Sense and Operations with Fractions and Decimals The student will be able to: The constructed-response component of the Mathematics tests assesses students’ ability to communicate in mathematics. At • Use place value in relation to decimal numbers, recognize this level, the work students will be able to do includes: plotting relative magnitude of fractions and decimals, and use points on a grid, estimating solutions, and graphically models to represent order of fractions and decimals. representing fractions. Level 3 Sample Question 24 & 25 • Add and subtract simple fractions and find half of an even number. * Available for CTP 4 only. • Solve real-life problems involving fractions and decimals, including money problems. Level 3 Sample Questions 21 & 22

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VERBAL REASONING Precision The student will be able to distinguish among subtle shades of The CTP Verbal Reasoning test at Level 4 measures students’ meaning in choosing the appropriate word or words to fill in ability to conceptualize relationships among words and the blank(s) in a sentence. concepts and to draw conclusions based on incomplete information. The ability to infer information that is not Application explicitly stated in a text is an essential aspect of fluency in The student will be able to: reading; the CTP Verbal Reasoning test at Level 4 evaluates • Understand the meaning of a word in the context of a students’ developing proficiency in this area. The following is a passage and identify the correct definition. list of the skills measured by the CTP Verbal Reasoning test at • Understand the meaning of a word in the context of a Level 4. passage and identify a synonym for that word. Analogical Reasoning • Understand the meaning of a word in the context of a The student will be able to: passage and identify an antonym of that word. • Recognize the relationship between two words and identify another pair of words with the same relationship. READING COMPREHENSION • Identify the definition that accurately describes the relationship between a pair of words. The CTP Reading Comprehension test at Level 4 measures students’ ability to understand and interpret written text. The Categorical Reasoning NCTE/IRA Standards for the English Language Arts emphasizes The student will be able to: the importance of being able to use a “wide range of strategies • Recognize which of several elements does or does not fit into to comprehend, interpret, evaluate, and appreciate text” (31). a thematically grouped list of words. The CTP Reading Comprehension test requires students to draw on these strategies to interpret and analyze a range of • Generalize about a thematically grouped list of words and texts, both fiction and nonfiction. The following is a list of the choose an appropriate heading for the list. skills measured by the CTP Reading Comprehension test at Level 4. Logical Reasoning The student will be able to: Explicit Information • Solve deductive ordering problems and draw conclusions The student will be able to: that are directly deducible from the information provided. • Use explicit information to identify the main idea or primary • Solve inductive reasoning problems by reasoning from purpose of a text or part of a text. details or evidence to a generalization or hypothesis that • Identify explicit details from a passage and provide answers makes sense of the evidence. to “who,” “what,”“where,”“when,”“why,” and “how” questions about the text.

VOCABULARY Inference The student will be able to: Reading fluency depends on both an extensive learned vocabulary and the ability to decode unfamiliar words. The • Use implicit information from a passage to make inferences CTP Vocabulary test at Level 4 measures students’ expanding about the motives or behaviors of characters. vocabulary and their developing ability to distinguish more • Use implicit information from a passage to answer specific subtle differences among related words. At Level 4, vocabulary questions about a text. words are tested exclusively in the context of a sentence or passage. The following is a list of the skills measured by the Analysis CTP Vocabulary test at Level 4. The student will be able to: • Determine whether information included in a passage Word Meaning consists of fact or opinion. The student will be able to: • Use explicit and implicit information to determine the • Understand the meaning of a word in the context of a author’s likely intent for writing a passage or for including sentence and identify the correct definition. certain information in a passage. • Understand the meaning of a word in the context of a • Synthesize explicit and implicit information to make sentence and identify a synonym for that word. predictions, draw conclusions, or formulate hypotheses • Understand the meaning of a word in the context of a about a text. sentence and identify an antonym of that word.

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READING COMPREHENSION CONTINUED WRITING MECHANICS

Reading for Understanding The development of a foundational understanding of language Optional Constructed-Response Section* conventions and mechanics is essential as students move from copying letters and words to writing sentences to composing Students use their developing productive language skills to paragraphs. The NCTE/IRAStandards for the English Language answer questions about text, employing comprehension Arts indicates that students should be able to “apply knowledge strategies to interpret and analyze the texts, describe of language structure and language conventions (e.g., spelling important aspects of the texts, synthesize information and punctuation) . . . to create, critique, and discuss print and from two texts, and compare and contrast elements within non-print texts” (36). The CTP Writing Mechanics test at Level a text and/or between two texts. At level 4, some questions 4 measures students’ growing understanding of English require students to make elementary inferences about sentence structure and language conventions. The following is information that is not explicitly stated in the text. The a list of the skills measured by the CTP Writing Mechanics test student will be able to: at Level 4. • Describe the main idea in a passage. • Describe a supporting idea in a passage. Spelling The student will be able to identify misspellings of commonly • Compare and contrast elements from two texts. used words, including words with affixes and words that • Make inferences about a character’s feelings or motivation. display improper pluralization. • Synthesize information from two texts to make predictions Capitalization or draw conclusions. The student will be able to recognize correct and incorrect capitalization. Specific rules tested include: NOTE: Although the Reading for Understanding section does require students to write their answers, it is a test of • Capitalization of proper nouns. reading comprehension and not writing ability. Students’ • Capitalization of the first word of a sentence. responses are evaluated based on how completely and thoroughly they answer the questions; misspellings, • Capitalization in titles and forms of address. grammatical mistakes, and other writing errors do not count against them. The questions are scored on a 0-2 Punctuation scale. The student will be able to recognize correct and incorrect punctuation. Specific rules tested include: * Available for CTP 4 only. • The correct use of the comma. • The correct use of the apostrophe in contractions and possessives. • Proper punctuation for dialogue and letter writing. • Correct end punctuation.

Usage The student will be able to apply rules of English diction and grammar. Specific rules tested include: • Correct pronoun use, including pronoun-antecedent agreement. • Correct verb form and tense, including subject-verb agreement and parallelism. • Rules of correct and effective expression at the sentence level, including proper modification. • Rules of diction within the context of a sentence. • Rules of sentence boundaries, including avoiding run-ons and fragments.

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WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 4 integrates The Quantitative Reasoning test assesses students’ ability to students’ developing facility with English grammar and usage engage, in age-level appropriate ways, in pattern recognition, with a growing understanding of writing and the writing classification, and reasoning in all content areas, including process. As students begin to develop more comprehensive logic, arithmetic, algebra, geometry, probability, and statistics paragraphs and to learn the stages of the writing process, the The following is a list of the skills measured by the CTP ability to organize complex information and to recognize the Quantitative Reasoning test at Level 4. multiple purposes and audiences for writing becomes increasingly important. According to the NCTE/IRA Standards Comparison for the English Language Arts, it is important that students be The student will be able to: able to “employ a wide range of strategies as they write and use • Consider numerical quantities in various forms and different writing process elements appropriately to compare their sizes. communicate with different audiences for a variety of purposes” (35). The following is a list of the skills measured by • Consider the relative measures of geometric shapes. the CTP Writing Concepts and Skills test at Level 4. • Recognize relative sizes of units of measure, including between systems. Organization The student will be able to: Extensions and Generalizations • Recognize thesis statements, topic sentences, and The student will be able to: conclusions. • Formulate arithmetic conclusions based on observation and • Recognize effective transitions between ideas, sentences, mathematical judgment. and paragraphs. • Formulate geometric conclusions based on observation and • Effectively and logically sequence information within a mathematical judgment. paragraph or passage. • Recognize patterns and geometric representation of real-life situations. Purpose, Audience, and Focus The student will be able to: Analysis • Recognize the role of the audience within varying contexts The student will be able to: and draw logical conclusions about the intended audience • Interpret symbolic representation of numerical quantities. for a given passage. • Interpret charts, graphs, statistical measures, and • Understand how the purpose for and focus of a piece of probability. writing help determine the kind of information included and the appropriate style and tone of the piece. • Model geometric transformations.

Supporting Details MATHEMATICS (PART 1 AND 2) The student will be able to: • Identify effective and relevant details to support a given idea The six content strands in the Level 4 Mathematics test are: 1) or thesis. Numbers and Operations with Whole Numbers; 2) Numbers and Operations with Fractions and Decimals; 3) Geometry and • Choose the appropriate main idea or topic sentence for a Spatial Sense; 4) Measurement; 5) Data Analysis, Statistics, paragraph. and Probability; and 6) Patterns, Functions, and Pre-Algebra. Some topics included in Level 4 but not in Level 3 are: Style and Craft • Using powers of ten. The student will be able to: • Understanding squares of numbers. • Effectively combine two or more sentences into one logical sentence. • Understanding properties such as the commutative property, associative property, and the use of parentheses. • Recognize and identify accurate and appropriate word choices in a piece of writing. • Comparing fractions with unlike denominators. • Recognize and identify well-crafted sentences that exhibit • Modeling simple percents such as 25%, 50%, and 75%. rhetorical precision. • Adding and subtracting fractions with like denominators or simple fractions with unlike denominators (e.g., halves and fourths). • Naming and describing simple three-dimensional figures.

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Geometry and Spatial Sense MATHEMATICS CONTINUED The student will be able to: • Naming the types of angles. • Use basic geometric language to describe and name shapes, • Understanding a wider range of units of measurement, such and identify segments, rays, lines, and angles. as some units of capacity and mass. • Understand basic properties of figures, including number of • Finding the mean, median, and mode of a set of data. sides, vertices, angles, edges, and faces and characterize lines as intersecting, parallel, or perpendicular and angles • Using simple sample spaces to find probabilities. as right, acute, or obtuse. • Using basic counting techniques. • Identify relationships between figures and images under • Understanding the concept of a variable. transformation and identify lines of symmetry and the Along with subscores in the content strands, students will effects of combining, subdividing, and changing basic receive subscores in three process areas: Conceptual shapes. Understanding, Procedural Knowledge, and Problem Solving. In addition, students receive a subscore in Mathematics Measurement Communication if they take the constructed-response The student will be able to: component of the achievement test (available for CTP 4 only). • Understand approximate sizes in customary and metric The following is a list of the skills measured by the CTP units and the relationships between measures within the Mathematics test at Level 4. same system. • Use appropriate units of measurement and appropriate tools Number Sense and Operations with Whole Numbers for a given measurement. The student will be able to: • Understand the basic measure of perimeter and area. • Use place value; read, write, and compare whole numbers; use models to represent, order, and compare whole • Solve real-life problems involving elapsed time, calendars, numbers. temperature, capacity, weight, distance, or map scale. • Understand expanded notation, powers of ten, and squares of numbers. Data Analysis, Statistics, and Probability The student will be able to: • Perform arithmetic operations on whole numbers, know the language of basic operations, understand the relationship • Read and interpret various types of simple graphs, including between addition and multiplication, and estimate sums, bar, line, circle, pictorial, tables, and tallies. difference, products, and quotients. • Understand and compute mean, median, mode, and range. • Understand the properties of arithmetic operations, • Understand the concept of chance and basic counting including operations with zero, understand even and odd techniques used to describe an event. numbers, and multiply by multiples of 10. • Solve real-life problems involving number operations and Patterns, Functions, and Pre-Algebra rate problems. The student will be able to: • Recognize a wide variety of patterns and the rules that Number Sense and Operations with Fractions and Decimals explain them and understand graphs of coordinates. The student will be able to: • Solve simple open sentences, including inequalities and • Use place value in relation to decimal numbers, recognize select number sentences to represent problem situations. relative magnitude of fractions and decimals, use models to represent order of fractions and decimals, and estimate • Understand the basic concept of an equality relationship fractions and decimals with pictures. and the concept of a variable.

• Add and subtract decimals, simple fractions, and mixed Math Communication numbers. Optional Constructed-Response Section* • Multiply and divide amounts of money by a single digit and The constructed-response component of the Mathematics tests find half of an even number and a quarter of a multiple of 4. assesses students’ ability to communicate in mathematics. At • Solve real-life problems involving fractions and decimals. this level, the work students will be able to do includes: solving problems that involve multiplication and division, showing alternate ways to solve a problem, generalizing output of a function machine, and interpreting a Venn diagram.

* Available for CTP 4 only.

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VERBAL REASONING Precision The student will be able to distinguish among subtle shades of The CTP Verbal Reasoning test at Level 5 measures students’ meaning in choosing the appropriate word or words to fill in ability to conceptualize relationships among words and the blank(s) in a sentence. concepts and to draw conclusions based on incomplete information. The ability to infer information that is not Application explicitly stated in a text is an essential aspect of fluency in The student will be able to: reading; the CTP Verbal Reasoning test at Level 5 evaluates • Understand the meaning of a word in the context of a students’ developing proficiency in this area. The following is a passage and identify a synonym for that word. list of the skills measured by the CTP Verbal Reasoning test at • Understand the meaning of a word in the context of a Level 5. passage and identify an antonym of that word. Analogical Reasoning The student will be able to: READING COMPREHENSION • Recognize the relationship between two words and identify another pair of words with the same relationship. The CTP Reading Comprehension test at Level 5 measures • Identify the definition that accurately describes the students’ ability to understand and interpret written text. The relationship between a pair of words. NCTE/IRA Standards for the English Language Arts emphasizes the importance of being able to use a “wide range of strategies Categorical Reasoning to comprehend, interpret, evaluate, and appreciate text” (31). The student will be able to: The CTP Reading Comprehension test requires students to draw on these strategies to interpret and analyze a range of • Recognize which of several elements does or does not fit into texts, both fiction and nonfiction. The following is a list of the a thematically grouped list of words. skills measured by the CTP Reading Comprehension test at • Generalize about a thematically grouped list of words and Level 5. choose an appropriate heading for the list. Explicit Information Logical Reasoning The student will be able to: The student will be able to: • Use explicit information to identify the main idea or primary • Solve deductive ordering problems and draw conclusions purpose of a text or part of a text. that are directly deducible from the information provided. • Identify explicit details from a passage and provide answers • Solve inductive reasoning problems by reasoning from to “who,” “what,”“where,”“when,”“why,” and “how” details or evidence to a generalization or hypothesis that questions about the text. makes sense of the evidence. • Understand connections between and among explicit pieces of information from a passage. VOCABULARY • Put pieces of information from the passage in the correct chronological order. Reading fluency depends on both an extensive learned vocabulary and the ability to decode unfamiliar words. The Inference CTP Vocabulary test at Level 5 measures students’ expanding The student will be able to: vocabulary and their developing ability to distinguish more • Use implicit information from a passage to make inferences subtle differences among related words. At Level 5, vocabulary about the motives or behaviors of characters. words are tested exclusively in the context of a sentence or • Use implicit information from a passage to answer specific passage. The following is a list of the skills measured by the questions about a text. CTP Vocabulary test at Level 5.

Word Meaning The student will be able to: • Understand the meaning of a word in the context of a sentence and identify the correct definition. • Understand the meaning of a word in the context of a sentence and identify a synonym for that word. • Understand the meaning of a word in the context of a sentence and identify an antonym of that word.

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READING COMPREHENSION CONTINUED WRITING MECHANICS

Analysis The development of a foundational understanding of language The student will be able to: conventions and mechanics is essential as students begin to write more complex texts. The NCTE/IRAStandards for the • Determine whether information included in a passage English Language Arts indicates that students should be able to consists of fact or opinion. “apply knowledge of language structure and language • Use explicit and implicit information to determine the conventions (e.g., spelling and punctuation) . . . to create, author’s likely intent for writing a passage or for including critique, and discuss print and non-print texts” (36). The CTP certain information in a passage. Writing Mechanics test at Level 5 measures students’ growing • Recognize cause-and-effect relationships among elements understanding of English sentence structure and language in a text. conventions. The following is a list of the skills measured by the CTP Writing Mechanics test at Level 5. • Categorize and combine pieces of information in a text. • Synthesize explicit and implicit information to make Spelling predictions, draw conclusions, or formulate hypotheses The student will be able to identify misspellings of commonly about a text. used words, including words with affixes and words that display improper pluralization. Reading for Understanding Optional Constructed-Response Section* Capitalization The student will be able to recognize correct and incorrect Students use their developing productive language skills to capitalization. Specific rules tested include: answer questions about text, employing comprehension strategies to interpret and analyze the texts, describe • Capitalization of proper nouns. important aspects of the texts, synthesize information from • Capitalization of the first word of a sentence. two texts, and compare and contrast elements within a text and/or between two texts. At level 5, some questions require • Capitalization in titles and forms of address. students to make inferences about information that is not explicitly stated in the text. The student will be able to: Punctuation The student will be able to recognize correct and incorrect • Describe the main idea in a passage. punctuation. Specific rules tested include: • Describe a supporting idea in a passage. • The correct use of the comma. • Compare and contrast elements from two texts. • The correct use of the apostrophe in contractions and • Make inferences about a character’s feelings or motivation. possessives. • Synthesize information from two texts to make predictions • Proper punctuation for dialogue and letter writing. or draw conclusions. • Correct end punctuation.

NOTE: Although the Reading for Understanding section Usage does require students to write their answers, it is a test of The student will be able to apply rules of English diction and reading comprehension and not writing ability. Students’ grammar. Specific rules tested include: responses are evaluated based on how completely and thoroughly they answer the questions; misspellings, • Correct pronoun use, including pronoun-antecedent grammatical mistakes, and other writing errors do not agreement. count against them. The questions are scored on a 0-2 scale. • Correct verb form and tense, including subject-verb agreement and parallelism. * Available for CTP 4 only. • Rules of correct and effective expression at the sentence level, including proper modification. • Rules of diction within the context of a sentence. • Rules of sentence boundaries, including avoiding run-ons and fragments.

22 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 5

WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 5 integrates The Quantitative Reasoning test assesses students’ ability to students’ developing facility with English grammar and usage engage, in age-level appropriate ways, in pattern recognition, with a growing understanding of writing and the writing classification, and reasoning in all content areas, including process. As students continue to develop their writing skills logic, arithmetic, algebra, geometry, probability, and statistics and to learn the stages of the writing process, the ability to The following is a list of the skills measured by the CTP organize complex information and to recognize the multiple Quantitative Reasoning test at Level 5. purposes and audiences for writing becomes increasingly important. According to the NCTE/IRA Standards for the Comparison English Language Arts, it is important that students be able to The student will be able to: “employ a wide range of strategies as they write and use • Consider numerical quantities in various forms and different writing process elements appropriately to compare their sizes. communicate with different audiences for a variety of purposes” (35). The following is a list of the skills measured by • Consider the relative measures of geometric shapes. the CTP Writing Concepts and Skills test at Level 5. • Recognize relative sizes of units of measure, including between systems. Organization The student will be able to: Extensions and Generalizations • Recognize thesis statements, topic sentences, and The student will be able to: conclusions. • Formulate arithmetic conclusions based on observation and • Recognize effective transitions between ideas, sentences, mathematical judgment. and paragraphs. • Formulate geometric conclusions based on observation and • Effectively and logically sequence information within a mathematical judgment. paragraph or passage. • Recognize patterns and geometric representation of real-life situations. Purpose, Audience, and Focus The student will be able to: Analysis • Recognize the role of the audience within varying contexts The student will be able to: and draw logical conclusions about the intended audience • Interpret symbolic representation of numerical quantities. for a given passage. • Evaluate statistical arguments. • Understand how the purpose for and focus of a piece of writing help determine the kind of information included and • Model geometric transformations. the appropriate style and tone of the piece. MATHEMATICS (PART 1 AND 2) Supporting Details The student will be able to: The seven content strands in the Level 5 Mathematics test are: • Identify effective and relevant details to support a given idea 1) Numbers and Number Relationships; 2) Number Systems or thesis. and Number Theory; 3) Geometry and Spatial Sense; 4) Measurement; 5) Statistics; 6) Probability; and • Choose the appropriate main idea or topic sentence for a 7) Pre-Algebra. The Number Sense and Operations strands paragraph. from Levels 1 through 4 are replaced at Level 5 with two new number strands, recognizing the more advanced work at this Style and Craft level in arithmetic and properties of numbers. The Data strand The student will be able to: from Levels 1 through 4 has been divided at Level 5 into two • Recognize and identify accurate and appropriate word strands, reflecting the increased emphasis on statistics and choices in a piece of writing. probability. The Patterns strand from Levels 1 through 4 has been replaced with Pre-Algebra, recognizing the move at this • Recognize and identify well-crafted sentences that exhibit level toward more formal algebra. Some topics included in rhetorical precision. Level 5 but not in Level 4 are: • Using expanded notation and exponential forms of numbers. • Working with percents: • Understanding order of operations. • Understanding prime numbers and composite numbers.

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Measurement MATHEMATICS CONTINUED The student will be able to: • Understanding least common multiple and greatest • Understand systems of measurement and the relationships common factor. among units of the same system. • Adding and subtracting fractions with unlike denominators. • Use units appropriately and estimate measures using scale. • Understanding congruence and similarity. • Identifying lines, line segments, rays and angles. • Understand the measures of figures, including perimeter, • Using coordinate geometry. circumference, surface area, volume and angles (figures • Finding the range of a set of data. include rectangular solids). • Using Venn diagrams and tree diagrams. • Understand the application of formulas in deriving • Finding probabilities of related events. measures and solve simple rate problems. • Formulating equations from word sentences. • Applying the concepts of variable, expression, and equation Statistics to solve problems. The student will be able to:

Along with subscores in the content strands, students will • Read and interpret various types of simple graphs, including receive subscores in three process areas: Conceptual bar, single and double line, circle, pictorial, and tables. Understanding, Procedural Knowledge, and Problem Solving. • Understand and compute mean, median, mode, and range. In addition, students receive a subscore in Mathematics Communication if they take the constructed-response Probability component of the achievement test. The following is a list of the The student will be able to: skills measured by the CTP 4 Mathematics test at Level 5. • Determine probabilities, solve problems of chance using ratios and related probabilities, and make predictions based Numbers and Number Relationships on mathematical probabilities. The student will be able to: • Understand counting techniques, including the use of • Understand equivalent forms of fractions, decimals, and probability to determine amounts. percents and use number sense for numbers in these forms. • Understand multiple representation of numbers, including Pre-Algebra expanded notation and exponential forms. The student will be able to: • Apply numbers using multiple representations and • Represent patterns and mathematical situations involving understand plotting fractions on a real number line. tables, graphs, and equations. • Understand the use of variables, balancing equations, and Number Systems and Number Theory completing simple mathematical sentences to find an The student will be able to: unknown. • Understand place value with whole numbers and decimals • Apply variables, expressions, and equations to solve and recognize ordering of fractions and decimals. real-world problems and formulate equations from word • Understand multiples, factors, primes, and composites. sentences.

• Understand order of operations with whole numbers. Math Communication • Apply operations with fractions and decimals and number Optional Constructed-Response Section* theory concepts in everyday mathematical situations. The constructed-response component of the Achievement tests assesses students’ ability to communicate in mathematics. At Geometry and Spatial Sense this level, the work students will be able to do includes: solving The student will be able to: rate problems, evaluating strategies used to solve a problem, • Use basic geometric language to identify, describe, and and displaying information that satisfies given constraints. name shapes. * Available for CTP 4 only. • Understand basic characteristics and properties of figures, including applications in coordinate geometry. • Apply geometric properties and relationships, including congruence of figures, lines of symmetry, sum of angle measures in a triangle, images, under transformation, and two- and three-dimensional shape changes.

24 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 6 Sample Questions on pages 63-75

VERBAL REASONING • Understand the meaning of a word in the context of a sentence and identify an antonym of that word. The CTP Verbal Reasoning test at Level 6 measures students’ ability to conceptualize relationships among words and Precision concepts and to draw conclusions based on incomplete The student will be able to distinguish among subtle shades of information. The ability to infer information that is not meaning in choosing the appropriate word or words to fill in explicitly stated in a text is an essential aspect of fluency in the blank(s) in a sentence. Levels 4-6 Sample Questions 4 & 5 reading; the CTP Verbal Reasoning test at Level 6 evaluates students’ developing proficiency in this area. The following is a Application list of the skills measured by the CTP Verbal Reasoning test at The student will be able to: Level 6. • Understand the meaning of a word in the context of a passage and identify the correct definition of that word. Analogical Reasoning • Understand the meaning of a word in the context of a The student will be able to: passage and identify a synonym for that word. • Recognize the relationship between two words and identify • Understand the meaning of a word in the context of a another pair of words with the same relationship. Levels 4-6 passage and identify an antonym of that word. Sample Question 1 • Identify the definition that accurately describes the relationship between a pair of words. READING COMPREHENSION

Categorical Reasoning The CTP Reading Comprehension test at Level 6 measures The student will be able to: students’ ability to understand and interpret written text. The • Recognize which of several elements does or does not fit into NCTE/IRA Standards for the English Language Arts emphasizes a thematically grouped list of words. Levels 4-6 Sample the importance of being able to use a “wide range of strategies Question 2 to comprehend, interpret, evaluate, and appreciate text” (31). The CTP Reading Comprehension test requires students to • Generalize about a thematically grouped list of words and draw on these strategies to interpret and analyze a range of choose an appropriate heading for the list. texts, both fiction and nonfiction. The following is a list of the skills measured by the CTP Reading Comprehension test at Logical Reasoning Level 6. The student will be able to: • Solve deductive ordering problems and draw conclusions Explicit Information that are directly deducible from the information provided. The student will be able to: Levels 4-6 Sample Question 3 • Use explicit information to identify the main idea or primary • Solve inductive reasoning problems by reasoning from purpose of a text or part of a text. details or evidence to a generalization or hypothesis that • Identify explicit details from a passage and provide answers makes sense of the evidence. to “who,” “what,”“where,”“when,”“why,” and “how” questions about the text. Levels 4-6 Sample Questions 6, 7, 8, 11, & 12 VOCABULARY • Understand connections between and among explicit pieces Reading fluency depends on both an extensive learned of information from a passage. vocabulary and the ability to decode unfamiliar words. The • Put pieces of information from the passage in the correct CTP Vocabulary test at Level 6 measures students’ expanding chronological order. vocabulary and their developing ability to distinguish more subtle differences among related words. At Level 6, vocabulary Inference words are tested exclusively in the context of a sentence or The student will be able to: passage. The following is a list of the skills measured by the • Use implicit information from a passage to make inferences CTP Vocabulary test at Level 6. about the motives or behaviors of characters. Levels 4-6 Sample Question 13 Word Meaning The student will be able to: • Use implicit information from a passage to answer specific questions about a text. • Understand the meaning of a word in the context of a sentence and identify the correct definition. • Understand the meaning of a word in the context of a sentence and identify a synonym for that word.

25 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 6 Sample Questions on pages 63-75

READING COMPREHENSION CONTINUED WRITING MECHANICS

Analysis The development of a foundational understanding of language The student will be able to: conventions and mechanics is essential as students begin to write more complex texts. The NCTE/IRAStandards for the • Determine whether information included in a passage English Language Arts indicates that students should be able to consists of fact or opinion. Levels 4-6 Sample Question 9 “apply knowledge of language structure and language • Use explicit and implicit information to determine the conventions (e.g., spelling and punctuation) . . . to create, author’s likely intent for writing a passage or for including critique, and discuss print and non-print texts” (36). The CTP certain information in a passage. Writing Mechanics test at Level 6 measures students’ growing • Compare and contrast elements in a text. understanding of English sentence structure and language conventions. The following is a list of the skills measured by • Categorize and combine pieces of information in a text. the CTP Writing Mechanics test at Level 6. • Synthesize explicit and implicit information to make predictions, draw conclusions, or formulate hypotheses Spelling about a text. Levels 4-6 Sample Questions 10 & 14 The student will be able to identify misspellings of commonly used words, including words with affixes and words that Reading for Understanding display improper pluralization. Levels 4-6 Sample Question Optional Constructed-Response Section* 17 Students use their developing productive language skills to Capitalization answer questions about text, employing comprehension The student will be able to recognize correct and incorrect strategies to interpret and analyze the texts, describe capitalization. Specific rules tested include: important aspects of the texts, synthesize information from two texts, and compare and contrast elements within a text • Capitalization of proper nouns. and/or between two texts. At level 6, most questions require • Capitalization of the first word of a sentence. students to make inferences about information that is not explicitly stated in the text. The student will be able to: • Capitalization in titles and forms of address.

• Describe the main idea in a passage. Punctuation • Describe the overall theme of a passage. The student will be able to recognize correct and incorrect punctuation. Specific rules tested include: • Describe a supporting idea in a passage. Levels 4-6 Sample Question 15 • The correct use of the comma. • Compare and contrast elements from two texts. Levels 4-6 • The correct use of the apostrophe in contractions and Sample Question 16 possessives. Levels 4-6 Sample Question 18 • Make inferences about a character’s feelings or motivation. • Proper punctuation for dialogue and letter writing. • Synthesize information from two texts to describe • Correct end punctuation. supporting ideas, make predictions, or draw conclusions. Usage NOTE: Although the Reading for Understanding section The student will be able to apply rules of English diction and does require students to write their answers, it is a test of grammar. Specific rules tested include: reading comprehension and not writing ability. Students’ • Correct pronoun use, including pronoun-antecedent responses are evaluated based on how completely and agreement. thoroughly they answer the questions; misspellings, grammatical mistakes, and other writing errors do not • Correct verb form and tense, including subject-verb count against them. The questions are scored on a 0-2 agreement and parallelism. scale. • Rules of correct and effective expression at the sentence * Available for CTP 4 only. level, including proper modification. • Rules of diction within the context of a sentence. Levels 4-6 Sample Question 19 • Rules of sentence boundaries, including avoiding run-ons and fragments. Levels 4-6 Sample Question 20

26 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 6 Sample Questions on pages 63-75

WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 6 integrates The Quantitative Reasoning test assesses students’ ability to students’ developing facility with English grammar and usage engage, in age-level appropriate ways, in pattern recognition, with a growing understanding of writing and the writing classification, and reasoning in all content areas including process. As students continue to develop their writing skills logic, arithmetic, algebra, geometry, probability, and statistics. and to learn the stages of the writing process, the ability to The following is a list of the skills measured by the CTP organize complex information and to recognize the multiple Quantitative Reasoning test at Level 6. purposes and audiences for writing becomes increasingly important. According to the NCTE/IRA Standards for the Comparison English Language Arts, it is important that students be able to The student will be able to: “employ a wide range of strategies as they write and use • Consider numerical quantities in various forms and different writing process elements appropriately to compare their sizes. communicate with different audiences for a variety of purposes” (35). The following is a list of the skills measured by • Consider the relative measures of geometric shapes. Levels the CTP Writing Concepts and Skills test at Level 6. 4-6 Sample Question 26 • Recognize relative sizes of units of measure, including Organization between systems. The student will be able to: • Recognize thesis statements, topic sentences, and Extensions and Generalizations conclusions. The student will be able to: • Recognize effective transitions between ideas, sentences, • Formulate arithmetic conclusions based on observation and and paragraphs. mathematical judgment. Levels 4-6 Sample Question 27 • Effectively and logically sequence information within a • Formulate geometric conclusions based on observation and paragraph or passage. Levels 4-6 Sample Questions 21 & 22 mathematical judgment. • Recognize patterns and geometric representation of real-life Purpose, Audience, and Focus situations. The student will be able to: • Recognize the role of the audience within varying contexts Analysis and draw logical conclusions about the intended audience The student will be able to: for a given passage. • Interpret symbolic representation of numerical quantities. • Understand how the purpose for and focus of a piece of Levels 4-6 Sample Question 28 writing help determine the kind of information included and • Evaluate statistical arguments. the appropriate style and tone of the piece. Levels 4-6 Sample Question 23 • Model geometric transformations. Levels 4-6 Sample Question 29 Supporting Details The student will be able to: • Identify effective and relevant details to support a given idea or thesis. Levels 4-6 Sample Question 24 • Choose the appropriate main idea or topic sentence for a paragraph. Levels 4-6 Sample Question 25

Style and Craft The student will be able to: • Recognize and identify accurate and appropriate word choices in a piece of writing. • Recognize and identify well-crafted sentences that exhibit rhetorical precision.

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MATHEMATICS (PART 1 AND 2) measures in a triangle, triangle inequality, images under transformation, and two- and three- dimensional shape The seven content strands in the Level 6 Mathematics test are: changes. 1) Numbers and Number Relationships; 2) Number Systems and Number Theory; 3) Geometry and Spatial Sense; 4) Measurement Measurement; 5) Statistics; 6) Probability; and 7) Pre-Algebra. The student will be able to: Some topics included in Level 6 but not in Level 5 are: • Understand systems of measurement and the relationships • Using scientific notation to represent numbers. among units of the same system. • Understanding similarity of geometric figures. • Use units appropriately and estimate measures using scale. • Using the triangle inequality. • Understand the measures of figures, including perimeter, circumference, surface area, volume, and angles (figures • Understanding the volume and surface area of triangular include rectangular and triangular solids). Levels 4-6 prisms. Sample Questions 34, 35, & 36 • Understanding the volume of cylinders. • Understand the application of formulas in deriving measures and solve simple rate problems. Along with subscores in the content strands, students will receive subscores in three process areas: Conceptual Statistics Understanding, Procedural Knowledge, and Problem Solving. The student will be able to: In addition, students receive a subscore in Mathematics Communication if they take the constructed-response • Read and interpret various types of simple graphs, including component of the achievement test (available for CTP 4 only). bar, single and double line, circle, pictorial, and tables. The following is a list of the skills measured by the CTP • Understand and compute mean, median, mode, and range. Mathematics test at Level 6. Levels 4-6 Sample Questions 37 & 38

Numbers and Number Relationships Probability The student will be able to: The student will be able to: • Understand equivalent forms of fractions, decimals, and • Determine probabilities, solve problems of chance using percents and use number sense for numbers in these forms. ratios and related probabilities, and make predictions based Levels 4-6 Sample Question 30 on mathematical probabilities. Levels 4-6 Sample Question • Understand multiple representation of numbers, including 39 expanded notation, exponential forms, and scientific • Understand counting techniques, including the use of notation. probability to determine amounts. • Apply numbers using multiple representations and understand plotting fractions on a real number line. Pre-Algebra The student will be able to: Number Systems and Number Theory • Represent patterns and mathematical situations involving The student will be able to: tables, graphs, and equations. • Understand place value with whole numbers and decimals • Understand the use of variables, balancing equations, and and recognize ordering of fractions and decimals. completing simple mathematical sentences to find an • Understand multiples, factors, primes, and composites. unknown. • Understand order of operations with whole numbers. • Apply variables, expressions, and equations to solve real-world problems and formulate equations from word • Apply operations with fractions and decimals and number sentences. theory concepts in everyday mathematical situations. Levels 4-6 Sample Question 31 Math Communication Optional Constructed-Response Section* Geometry and Spatial Sense The student will be able to: The constructed-response component of the Mathematics tests assesses students’ ability to communicate in mathematics. At • Use basic geometric language to describe and name shapes. this level, the work students will be able to do includes: using Levels 4-6 Sample Question 32 mathematical argument to support a conclusion, representing • Understand basic properties of figures, including percents in a circle graph, and supplying an example to applications in coordinate geometry. Levels 4-6 Sample demonstrate a statistical problem. Levels 4-6 Sample Question 33 Questions 40 & 41 • Apply geometric properties and relationships, including * Available for CTP 4 only. congruence of figures, lines of symmetry, sum of angle

28 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 7 Sample Questions on pages 76-90

VERBAL REASONING Application The CTP Verbal Reasoning test at Level 7 measures students’ The student will be able to: ability to conceptualize relationships among words and • Understand the meaning of a word in the context of a concepts and to draw conclusions based on incomplete passage and identify the correct definition of that word. information. The ability to infer information that is not • Understand the meaning of a word in the context of a explicitly stated in a text is an essential aspect of fluency in passage and identify a synonym for that word. Levels 7-10 reading; the CTP Verbal Reasoning test at Level 7 evaluates Sample Questions 7-10 students’ developing proficiency in this area. The following is a list of the skills measured by the CTP Verbal Reasoning test at • Understand the meaning of a word in the context of a Level 7. passage and identify an antonym of that word.

Analogical Reasoning The student will be able to: READING COMPREHENSION The CTP Reading Comprehension test at Level 7 measures • Recognize the relationship between two words and identify students’ ability to understand and interpret written text. The another pair of words with the same relationship. NCTE/IRA Standards for the English Language Arts emphasizes • Identify the definition that accurately describes the the importance of being able to use a “wide range of strategies relationship between a pair of words. to comprehend, interpret, evaluate, and appreciate text” (31). The CTP Reading Comprehension test requires students to Categorical Reasoning draw on these strategies to interpret and analyze a range of The student will be able to: texts, both fiction and nonfiction. The following is a list of the • Recognize which of several elements does or does not fit into skills measured by the CTP Reading Comprehension test at a thematically grouped list of words. Level 7.

• Generalize about a thematically grouped list of words and Explicit Information choose an appropriate heading for the list. The student will be able to:

Logical Reasoning • Use explicit information to identify the main idea or primary The student will be able to: purpose of a text or part of a text. • Solve deductive ordering problems and draw conclusions • Identify explicit details from a passage and provide answers that are directly deducible from the information provided. to “who,” “what,”“where,”“when,”“why,” and “how” questions about the text. • Solve inductive reasoning problems by reasoning from details or evidence to a generalization or hypothesis that • Understand connections between and among explicit pieces makes sense of the evidence. of information from a passage. • Put pieces of information from the passage in the correct chronological order. VOCABULARY Reading fluency depends on both an extensive learned Inference vocabulary and the ability to decode unfamiliar words. The student will be able to: The CTP Vocabulary test at Level 7 measures students’ • Use implicit information from a passage to make inferences expanding vocabulary and their developing ability to about the motives or behaviors of characters. distinguish more subtle differences among related words. At Level 7, vocabulary words are tested both in and out of • Use implicit information from a passage to answer specific context. The following is a list of the skills measured by the questions about a text. CTP Vocabulary test at Level 7. Analysis Word Meaning The student will be able to: The student will be able to: • Determine whether information included in a passage • Identify a synonym for a word, either in the context of a consists of fact or opinion. sentence or alone. • Use explicit and implicit information to determine the • Identify an antonym of a word, either in the context of a author’s likely intent for writing a passage or for including sentence or alone. certain information in a passage. • Compare and contrast elements in a text. Precision The student will be able to distinguish among subtle shades of • Categorize and combine pieces of information in a text. meaning in choosing the appropriate word or words to fill in • Synthesize explicit and implicit information to make the blank(s) in a sentence. predictions, draw conclusions, or formulate hypotheses about a text.

29 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 7 Sample Questions on pages 76-90

READING COMPREHENSION CONTINUED WRITING MECHANICS

Reading for Understanding The development of an increasingly sophisticated *Optional Constructed-Response Section* understanding of language conventions and mechanics is essential as students continue to write more and more Students use their developing productive language skills to complex texts. The NCTE/IRA Standards for the English answer questions about text, employing comprehension Language Arts indicates that students should be able to “apply strategies to interpret and analyze the texts, describe knowledge of language structure and language conventions important aspects of the texts, synthesize information from (e.g., spelling and punctuation) . . . to create, critique, and two texts, and compare and contrast elements within a text discuss print and non-print texts” (36). The CTP Writing and/or between two texts. At level 7, most questions require Mechanics test at Level 7 measures students’ growing facility students to make inferences about information that is not with English sentence structure and language conventions. explicitly stated in the text. The student will be able to: The following is a list of the skills measured by the CTP Writing • Describe the main idea in a passage. Mechanics test at Level 7. • Describe the overall theme of a passage. Spelling, Capitalization, and Punctuation • Describe a supporting idea in a passage. The student will be able to recognize spelling, capitalization, • Compare and contrast elements from two texts. and punctuation errors. Specific elements tested include: • Make inferences about a character’s feelings or motivation. • Spelling of commonly used words, including words with affixes and words that display improper pluralization. • Make inferences about the author’s purpose. • Capitalization of proper nouns. • Synthesize information from two texts to describe supporting ideas, make predictions, or draw conclusions. • Capitalization in titles and forms of address. • The correct use of the comma, semicolon, and colon. NOTE: Although the Reading for Understanding section does require students to write their answers, it is a test of • The correct use of the apostrophe in contractions and reading comprehension and not writing ability. Students’ possessives. responses are evaluated based on how completely and • Proper punctuation for dialogue and letter writing. thoroughly they answer the questions; misspellings, grammatical mistakes, and other writing errors do not • Correct end punctuation. count against them. The questions are scored on a 0-2 scale. Usage The student will be able to apply rules of English diction and * Available for CTP 4 only. grammar. Specific rules tested include: • Correct pronoun use, including pronoun-antecedent agreement. • Correct verb form and tense, including subject-verb agreement and parallelism. • Rules of correct and effective expression at the sentence level, including proper modification. • Rules of diction within the context of a sentence.

Sentence Construction The student will be able to apply rules regarding sentence boundaries, including recognizing run-on sentences and sentence fragments.

30 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] CONTENT CATEGORIES: LEVEL 7 Sample Questions on pages 76-90

WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 7 integrates The Quantitative Reasoning test assesses students’ ability to students’ developing facility with English grammar and usage engage, in age-level appropriate ways, in pattern recognition, with a growing understanding of writing and the writing classification, and reasoning in all content areas including process. As students continue to develop their writing skills logic, arithmetic, algebra, geometry, probability, and statistics. and to learn the stages of the writing process, the ability to The following is a list of the skills measured by the CTP organize complex information and to recognize the multiple Quantitative Reasoning test at Level 7. purposes and audiences for writing becomes increasingly important. According to the NCTE/IRA Standards for the Comparison English Language Arts, it is important that students be able to The student will be able to: “employ a wide range of strategies as they write and use • Consider numerical quantities in various forms and different writing process elements appropriately to compare their sizes. communicate with different audiences for a variety of purposes” (35). The following is a list of the skills measured by • Consider the relative measures of geometric shapes. the CTP Writing Concepts and Skills test at Level 7. Extensions and Generalizations Organization The student will be able to: The student will be able to: • Formulate arithmetic conclusions based on observation and • Recognize thesis statements, topic sentences, and mathematical judgment. conclusions. • Formulate geometric conclusions based on observation and • Recognize effective transitions between ideas, sentences, mathematical judgment. and paragraphs. • Recognize patterns and geometric representation of real-life • Effectively and logically sequence information within a situations. paragraph or passage. Analysis Purpose, Audience, and Focus The student will be able to: The student will be able to: • Interpret algebraic representations. • Recognize the role of the audience within varying contexts • Evaluate statistical arguments, including counting and draw logical conclusions about the intended audience principles and basic interpretation of probabilities. for a given passage. • Model geometric transformations. • Understand how the purpose for and focus of a piece of writing help determine the kind of information included and the appropriate style and tone of the piece.

Supporting Details The student will be able to: • Identify effective and relevant details to support a given idea or thesis. • Choose the appropriate main idea or topic sentence for a paragraph.

Style and Craft The student will be able to: • Recognize and identify accurate and appropriate word choices in a piece of writing. • Effectively combine two or more sentences into one logical sentence. • Recognize and identify well-crafted sentences that exhibit rhetorical precision.

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MATHEMATICS (PART 1 AND 2) Geometry and Spatial Sense The student will be able to: The content strands in the Level 7 Mathematics test are: 1) • Use basic geometric language to classify and characterize Numbers and Number Relationships; 2) Number Systems and properties of geometric figures. Number Theory; 3) Geometry; 4) Measurement; 5) Probability; • Apply geometric properties and relationships to two- and 6) Statistics; and 7) Pre-Algebra. Some topics included in Level three- dimensional figures, including the Pythagorean 7 but not in Level 6 are: Theorem, congruence and similarity of figures, lines of • Representing numbers in one- and two-dimensional graphs. symmetry, sum of angle measures in a triangle, triangle • Estimating square roots. inequality, and transformation in the coordinate plane.

• Applying theories of whole numbers, and signed numbers in Measurement context. The student will be able to: • Using the Pythagorean Theorem. • Apply concepts of measure, including perimeter, • Computing perimeter and area of irregular figures. circumference, surface area, volume, weight, and angle measure (figures include irregular shapes). • Solving linear equations and inequalities. • Use units appropriately and estimate measures using scale. Along with subscores in the content strands, students • Develop formulas to solve problems of measure and solve will receive subscores in three process areas: Conceptual simple rate problems. Understanding, Procedural Knowledge, and Problem Solving. In addition, students receive a subscore in Probability Mathematics Communication if they take the constructed- The student will be able to: response component of the achievement test (available for CTP 4 only). The following is a list of the skills measured by the CTP • Determine probabilities, solve problems of chance using Mathematics test at Level 7. ratios and related probabilities, and make predictions based on mathematical probabilities. Numbers and Number Relationships • Understand counting techniques, including the use of The student will be able to: permutations and combinations. • Understand equivalent forms of fractions, decimals, and percents; use estimates of these numbers and square roots; Statistics and use multiple representation of numbers, including The student will be able to: exponential and scientific notations. • Generate, organize, evaluate, and interpret various data • Recognize the form of a number appropriate for use in a representations. given situation and apply ratio, percent, and proportion in a • Understand and compute mean, median, mode, and range. variety of situations. • Represent number relationships in one- and two- Pre-Algebra dimensional graphs. The student will be able to: • Represent patterns and mathematical situations involving Number Systems and Number Theory tables, graphs, verbal rules, and equations. The student will be able to: • Solve simple linear equations and inequalities. • Recognize the need for numbers beyond whole numbers, including signed numbers, decimals, and fractions. • Apply variables, expressions, and equations to solve real-world problems and mathematical problems. • Identify perfect squares, factors, or multiples of integers, including least common multiple and greatest common Math Communication divisor. Optional Constructed-Response Section* • Apply operations with fractions, decimals, and signed The constructed-response component of the Mathematics tests numbers and number theory concepts in everyday assesses students’ ability to communicate in mathematics. At mathematical situations. this level, the work students will be able to do includes: • Understand order of arithmetic operations. showing application of the Pythagorean Theorem to solve a problem, placing fractions and decimals on a number line, and expressing a relationship algebraically.

* Available for CTP 4 only.

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VERBAL REASONING Application The student will be able to: The CTP Verbal Reasoning test at Level 8 measures students’ • Identify the correct definition of a word in the context of a ability to conceptualize relationships among words and passage. Levels 7-10 Sample Question 6 concepts and to draw conclusions based on incomplete • Identify a synonym or antonym of a word in the context of a information. The ability to infer information that is not passage. explicitly stated in a text is an essential aspect of fluency in reading; the CTP Verbal Reasoning test at Level 8 evaluates students’ developing proficiency in this area. The following is a list of the skills measured by the CTP Verbal Reasoning test at READING COMPREHENSION Level 8. The CTP Reading Comprehension test at Level 8 measures students’ ability to understand and interpret written text. The Analogical Reasoning NCTE/IRA Standards for the English Language Arts emphasizes The student will be able to: the importance of being able to use a “wide range of strategies • Recognize the relationship between two words and identify to comprehend, interpret, evaluate, and appreciate text” (31). another pair of words with the same relationship. Levels The CTP Reading Comprehension test requires students to 7-10 Sample Question 1 draw on these strategies to interpret and analyze a range of • Identify the definition that accurately describes the texts, both fiction and nonfiction. The following is a list of the relationship between a pair of words. skills measured by the CTP Reading Comprehension test at Level 8. Categorical Reasoning The student will be able to: Explicit Information The student will be able to: • Recognize which of several elements does or does not fit into a thematically grouped list of words. Levels 7-10 Sample • Use explicit information to identify the main idea or primary Question 2 purpose of a text or part of a text. • Generalize about a thematically grouped list of words and • Identify explicit details from a passage and provide answers choose an appropriate heading for the list. to “who,” “what,”“where,”“when,”“why,” and “how” questions about the text. Logical Reasoning • Understand connections between and among explicit pieces The student will be able to: of information from a passage. • Solve deductive ordering problems and draw conclusions • Put pieces of information from the passage in the correct that are directly deducible from the information provided. chronological order. Levels 7-10 Sample Question 3 • Solve inductive reasoning problems by reasoning from Inference details or evidence to a generalization or hypothesis that The student will be able to: makes sense of the evidence. • Use implicit information from a passage to make inferences about the motives or behaviors of characters. VOCABULARY • Use implicit information from a passage to answer specific questions about a text. Reading fluency depends on both an extensive learned vocabulary and the ability to decode unfamiliar words. Analysis The CTP Vocabulary test at Level 8 measures students’ The student will be able to: expanding vocabulary and their developing ability to distinguish more subtle differences among related words. • Determine whether information included in a passage At Level 8, vocabulary words are tested both in and out of consists of fact or opinion. context. The following is a list of the skills measured by the • Use explicit and implicit information to determine the CTP Vocabulary test at Level 8. author’s likely intent for writing a passage or for including certain information in a passage. Word Meaning The student will be able to identify synonyms and antonyms of • Synthesize explicit and implicit information to make words. predictions, draw conclusions, or formulate hypotheses about a text. Precision The student will be able to distinguish among subtle shades of meaning in choosing the appropriate word or words to fill in the blank(s) in a sentence. Levels 7-10 Sample Questions 4 & 5

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READING COMPREHENSION CONTINUED WRITING MECHANICS

Reading for Understanding The development of an increasingly sophisticated Optional Constructed-Response Section* understanding of language conventions and mechanics is essential as students continue to write more and more Students use their developing productive language skills to complex texts. The NCTE/IRA Standards for the English answer questions about text, employing comprehension Language Arts indicates that students should be able to “apply strategies to interpret and analyze the texts, describe knowledge of language structure and language conventions important aspects of the texts, synthesize information from (e.g., spelling and punctuation) . . . to create, critique, and two texts, and compare and contrast elements within a text discuss print and non-print texts” (36). The CTP Writing and/or between two texts. At level 8, most questions require Mechanics test at Level 8 measures students’ growing facility students to make inferences about information that is not with English sentence structure and language conventions. explicitly stated in the text. The student will be able to: The following is a list of the skills measured by the CTP • Describe the main idea or overall theme of a passage and/or Writing Mechanics test at Level 8. summarize the main points of a passage. • Describe a supporting idea in a passage. Levels 7-10 Sample Spelling, Capitalization, and Punctuation Question 22 The student will be able to recognize spelling, capitalization, and punctuation errors. Specific elements tested include: • Compare and contrast elements from two texts. • Spelling of commonly used words, including words with • Make inferences about a character’s motivation or the affixes and words that display improper pluralization. author’s purpose. Levels 7-10 Sample Question 24 • Synthesize information from two texts to describe • Capitalization of proper nouns and in titles and forms of supporting ideas, make predictions, or draw conclusions. address. Levels 7-10 Sample Question 23 • The correct use of the comma, semicolon, and colon. Levels NOTE: Although the Reading for Understanding section 7-10 Sample Question 25 does require students to write their answers, it is a test of • The correct use of the apostrophe in contractions and reading comprehension and not writing ability. Students’ possessives. responses are evaluated based on how completely and thoroughly they answer the questions; misspellings, • Proper punctuation for dialogue and quotations. grammatical mistakes, and other writing errors do not • Correct end punctuation. count against them. The questions are scored on a 0-2 scale. Usage The student will be able to apply rules of English diction and * Available for CTP 4 only. grammar. Specific rules tested include: • Correct pronoun use, including pronoun-antecedent agreement. • Correct verb form and tense, including subject-verb agreement and parallelism. • Rules of correct and effective expression at the sentence level, including proper modification. • Rules of diction within the context of a sentence. Levels 7-10 Sample Question 26

Sentence Construction The student will be able to apply rules regarding sentence boundaries, including recognizing run-on sentences and sentence fragments.

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WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 8 integrates The Quantitative Reasoning test assesses students’ ability to students’ developing facility with English grammar and usage engage, in age-level appropriate ways, in pattern recognition, with an increasingly sophisticated understanding of the classification, and reasoning in all content areas, including writing process. As students continue to develop their writing logic, arithmetic, algebra, geometry, probability, and statistics. skills, the ability to organize complex information and to The following is a list of the skills measured by the CTP recognize the multiple purposes and audiences for writing Quantitative Reasoning test at Level 8. becomes increasingly important. According to the NCTE/IRA Standards for the English Language Arts, it is important that Comparison students be able to “employ a wide range of strategies as they The student will be able to: write and use different writing process elements appropriately • Consider numerical quantities in various forms and to communicate with different audiences for a variety of compare their sizes. purposes” (35). The following is a list of the skills measured by the CTP Writing Concepts and Skills test at Level 8. • Consider the relative measures of geometric shapes. • Recognize relative sizes of units of measure, including Organization between systems. The student will be able to: • Recognize thesis statements, topic sentences, and Extensions and Generalizations conclusions. The student will be able to: • Recognize effective transitions between ideas, sentences, • Formulate arithmetic conclusions based on observation and and paragraphs. mathematical judgment. Levels 7-10 Sample Question 32 • Effectively and logically sequence information.Levels 7-10 • Formulate geometric conclusions based on observation and Sample Questions 27 & 28 mathematical judgment. • Recognize patterns logic problems, and geometric Purpose, Audience, and Focus representation of real-life situations. The student will be able to: • Recognize the role of the audience within varying contexts Analysis and draw logical conclusions about the intended audience The student will be able to: for a given passage. • Interpret algebraic representations. Levels 7-10 Sample • Understand how the purpose for and focus of a piece of Questions 33 & 34 writing help determine the kind of information included and • Evaluate statistical arguments, including counting the appropriate style and tone of the piece. Levels 7-10 principles and basic interpretation of probabilities. Sample Question 29

Supporting Details The student will be able to: • Identify effective and relevant details to support a given idea or thesis. • Choose the appropriate main idea or topic sentence for a paragraph. Levels 7-10 Sample Questions 30 & 31

Style and Craft The student will be able to: • Recognize and identify accurate and appropriate word choices in a piece of writing. • Effectively combine two or more sentences into one logical sentence. • Recognize and identify well-crafted sentences that exhibit rhetorical precision.

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MATHEMATICS (PART 1 AND 2) • Apply geometric properties and relationships to two- and three-dimensional figures including the Pythagorean The seven content strands in the Level 8 Mathematics test are: Theorem, congruence and similarity of figures, lines of 1) Numbers and Number Relationships; 2) Number Systems symmetry, sum of angle measures in a polygon, triangle and Number Theory; 3) Geometry; 4) Measurement; 5) inequality, and transformation in the coordinate plane. Probability; 6) Statistics; and 7) Pre-Algebra. At Level 8 there is Levels 7-10 Sample Question 38 an increased emphasis on questions in Pre-Algebra. Additionally, some topics included in Level 8 but not in Level 7 Measurement are: The student will be able to: • Using properties of three-dimensional figures. • Apply concepts of measure, including perimeter, circumference, surface area, volume, weight, and angle • Computing volume and surface area of irregular three- measure (figures include irregular shapes). dimensional figures. • Use units appropriately and estimate measures using scale. • Graphing lines in the coordinate plane. • Develop formulas to solve problems of measure and solve • Simplifying simple algebraic expressions. simple rate problems.

Along with subscores in the content strands, students will Probability receive subscores in three process areas: Conceptual The student will be able to: Understanding, Procedural Knowledge, and Problem Solving. In addition, students receive a subscore in Mathematics • Determine probabilities, solve problems of chance using Communication if they take the constructed-response ratios and related probabilities and make predictions based component of the achievement test (available for CTP 4 only). on mathematical probabilities. Levels 7-10 Sample The following is a list of the skills measured by the CTP Question 39 Mathematics test at Level 7. • Understand counting techniques including use of permutations and combinations. Numbers and Number Relationships The student will be able to: Statistics • Understand equivalent forms of fractions, decimals, and The student will be able to: percents; use estimates of these numbers and square roots; • Generate, organize, evaluate, and interpret various data and use multiple representation of numbers, including representations. exponential and scientific notations.Levels 7-10 Sample Question 35 • Understand and compute mean, median, mode, and range.

• Recognize the form of a number appropriate for use in a Pre-Algebra given situation and apply ratio, percent, and proportion in a The student will be able to: variety of situations. Levels 7-10 Sample Questions 36 & 37 • Represent patterns and mathematical situations involving • Represent number relationships in one- and two- tables, graphs, verbal rules, and equations. Levels 7-10 dimensional graphs. Sample Question 40

Number Systems and Number Theory • Solve simple linear equations and inequalities, simplify The student will be able to: algebraic expression and graph linear equations and inequalities on a number line or in the coordinate plane. • Recognize the need for numbers beyond whole numbers, Levels 7-10 Sample Question 41 including signed numbers, decimals, and fractions. • Apply variables, expressions and equations to solve real- • Identify perfect squares, factors, or multiples of integers, world problems and mathematical problems including including least common multiple and greatest common simple non-linear equations. Levels 7-10 Sample Questions divisor. 42 & 43 • Apply operations with fractions, decimals, and signed numbers and number theory concepts in everyday Math Communication mathematical situations. Optional Constructed-Response Section* • Understand order of arithmetic operations. The constructed-response component of the Mathematics tests assesses students’ ability to communicate in mathematics. At Geometry and Spatial Sense this level, the work students will be able to do includes: The student will be able to: drawing a three-dimensional solid resulting from a transformation, citing a counterexample to disprove a • Use basic geometric language to classify and characterize statement, and writing a linear equation from information properties of geometric figures including three-dimensional given about the line. Levels 7-10 Sample Questions 44 & 45 figures. * Available for CTP 4 only.

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ALGEBRA I

The Algebra I test is an end-of-course test and should be administered at the completion of a first-year course in Algebra. The four content strands in the Algebra I test are 1) Expressions, Statements, and Matrices; 2) Equations and Inequalities; 3) Tables, Graphs, and Algebraic Geometry; and 4) Situations Involving Variable Quantities. The following is a list of the skills measured by the CTP Algebra I test at Level 8.

Expressions, Statements, and Matrices The student will be able to: • Simplify algebraic expressions in various forms by applying arithmetic properties (forms include rational and exponential expressions). • Understand equivalent algebraic expressions, including expressions that are obtained by factoring. • Evaluate algebraic expressions for given values.

Equations and Inequalities The student will be able to: • Solve linear equations/inequalities, simple systems of linear equations, and literal equations for one variable. Levels 7-10 Sample Questions 46 & 47 • Identify arithmetic properties. • Apply algebraic equations to solve real-life problems and mathematical situations. • Solve simple quadratic equations. Levels 7-10 Sample Question 48 • Understand relationships of coefficients for equivalent quadratic expressions.

Tables, Graphs, and Algebraic Geometry The student will be able to: • Understand the xy-coordinate system and graphs of points, linear equations, and linear inequalities. Levels 7-10 Sample Question 49 • Identify linear equations and their characteristics, including slope and x- and y-intercepts. • Recognize relationships between parallel and perpendicular lines.

Situations Involving Variable Quantities The student will be able to translate real-life and mathematical situations into algebraic expressions or equations. Levels 7-10 Sample Question 50

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VERBAL REASONING Application The student will be able to: The CTP Verbal Reasoning test at Level 9 measures students’ • Understand the meaning of a word in the context of a ability to conceptualize relationships among words and passage and identify the correct definition of that word. concepts and to draw conclusions based on incomplete • Understand the meaning of a word in the context of a information. The ability to infer information that is not passage and identify a synonym for that word. explicitly stated in a text is an essential aspect of fluency in reading; the CTP Verbal Reasoning test at Level 9 evaluates • Understand the meaning of a word in the context of a students’ developing proficiency in this area. The following is a passage and identify an antonym of that word. list of the skills measured by the CTP Verbal Reasoning test at Level 9. READING COMPREHENSION Analogical Reasoning The student will be able to: The CTP Reading Comprehension test at Level 9 measures students’ ability to understand and interpret written text. The • Recognize the relationship between two words and identify NCTE/IRA Standards for the English Language Arts emphasizes another pair of words with the same relationship. the importance of being able to use a “wide range of strategies • Identify the definition that accurately describes the to comprehend, interpret, evaluate, and appreciate text” (31). relationship between a pair of words. The CTP Reading Comprehension test requires students to draw on these strategies to interpret and analyze a range of Categorical Reasoning texts, both fiction and nonfiction. The following is a list of the The student will be able to: skills measured by the CTP Reading • Recognize which of several elements does or does not fit into Comprehension test at Level 9. a thematically grouped list of words. Explicit Information • Generalize about a thematically grouped list of words and The student will be able to: choose an appropriate heading for the list. • Use explicit information to identify the main idea or primary Logical Reasoning purpose of a text or part of a text. Levels 7-10 Sample The student will be able to: Question 11 • Solve deductive ordering problems and draw conclusions • Identify explicit details from a passage and provide answers that are directly deducible from the information provided. to “who,” “what,”“where,”“when,”“why,” and “how” questions about the text. Levels 7-10 Sample Question 17 • Solve inductive reasoning problems by reasoning from details or evidence to a generalization or hypothesis that • Understand connections between and among explicit pieces makes sense of the evidence. of information from a passage.

Inference VOCABULARY The student will be able to: • Use implicit information from a passage to make inferences Reading fluency depends on both an extensive learned about the motives or behaviors of characters. vocabulary and the ability to decode unfamiliar words. • Use implicit information from a passage to answer specific The CTP Vocabulary test at Level 9 measures students’ questions about a text. Levels 7-10 Sample Questions 12, expanding vocabulary and their developing ability to 18, 19, & 20 distinguish more subtle differences among related words. At Level 9, vocabulary words are tested both in and out of context. The following is a list of the skills measured by the CTP Vocabulary test at Level 9.

Word Meaning The student will be able to identify synonyms and antonyms of words.

Precision The student will be able to distinguish among subtle shades of meaning in choosing the appropriate word or words to fill in the blank(s) in a sentence.

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READING COMPREHENSION CONTINUED WRITING MECHANICS

Analysis The development of an increasingly sophisticated The student will be able to: understanding of language conventions and mechanics is essential as students continue to write more and more • Determine whether information included in a passage complex texts. The NCTE/IRA Standards for the English consists of fact or opinion. Language Arts indicates that students should be able to “apply • Use explicit and implicit information to determine the knowledge of language structure and language conventions author’s likely intent for writing a passage or for including (e.g., spelling and punctuation) … to create, critique, and certain information in a passage. Levels 7-10 Sample discuss print and non-print texts” (36). The CTP Writing Questions 13, 14, 15, & 21 Mechanics test at Level 9 measures students’ growing facility • Compare and contrast elements in a text. with English sentence structure and language conventions. The following is a list of the skills measured by the CTP • Categorize and combine pieces of information in a text. Writing Mechanics test at Level 9. • Synthesize explicit and implicit information to make predictions, draw conclusions, or formulate hypotheses Spelling, Capitalization, and Punctuation about a text. The student will be able to recognize spelling, capitalization, and punctuation errors. Specific elements tested include: • Identify the style, tone, or theme of a text. Levels 7-10 Sample Question 16 • Spelling of commonly used words. • Capitalization of proper nouns. Reading for Understanding Optional Constructed-Response Section* • Capitalization in titles and forms of address. Students use their developing productive language skills to • The correct use of the comma, semicolon, and colon. answer questions about text, employing comprehension • The correct use of the apostrophe in contractions and strategies to interpret and analyze the texts, describe possessives. important aspects of the texts, synthesize information from • Proper punctuation for dialogue and quotations. two texts, and compare and contrast elements within a text and/or between two texts. At level 9, most questions require • Correct end punctuation. students to make inferences about information that is not explicitly stated in the text. At this level, students are also Usage asked to apply their growing understanding of figurative The student will be able to apply rules of English diction and language to answer some questions. The student will be able to: grammar. Specific rules tested include: • Correct pronoun use, including pronoun-antecedent • Describe the main idea or overall theme of a passage and/or agreement. summarize the main points of a passage. • Correct verb form and tense, including subject-verb • Describe the overall theme of a passage. agreement and parallelism. • Describe a supporting idea in a passage. • Rules of correct and effective expression at the sentence • Apply understanding of figurative language to describe level, including proper modification. aspects of a passage. • Rules of diction within the context of a sentence. • Compare and contrast elements from two texts. • Rules regarding sentence boundaries, including avoiding • Make inferences about a character’s motivation or the run-ons and fragments and recognizing sentence types. author’s purpose. • Synthesize information from two texts to describe supporting ideas, make predictions, or draw conclusions.

NOTE: Although the Reading for Understanding section does require students to write their answers, it is a test of reading comprehension and not writing ability. Students’ responses are evaluated based on how completely and thoroughly they answer the questions; misspellings, grammatical mistakes, and other writing errors do not count against them. The questions are scored on a 0-2 scale.

* Available for CTP 4 only.

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WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING

The CTP Writing Concepts and Skills test at Level 9 integrates The Quantitative Reasoning test assesses students’ ability to students’ developing facility with English grammar and usage engage, in age-level appropriate ways, in pattern recognition, with an increasingly sophisticated understanding of the classification, and reasoning in all content areas, including writing process. As students continue to develop their writing logic, arithmetic, algebra, geometry, probability, and statistics. skills, the ability to organize complex information and to The following is a list of the skills measured by the CTP recognize the multiple purposes and audiences for writing Quantitative Reasoning test at Level 9. becomes increasingly important. According to the NCTE/IRA Standards for the English Language Arts, it is important that Comparison students be able to “employ a wide range of strategies as they The student will be able to: write and use different writing process elements appropriately • Consider numerical quantities in various forms and to communicate with different audiences for a variety of compare their sizes. purposes” (35). The following is a list of the skills measured by the CTP Writing Concepts and Skills test at Level 9. • Consider the relative measures of geometric shapes.

Organization Extensions and Generalizations The student will be able to: The student will be able to: • Recognize thesis statements, topic sentences, and • Formulate arithmetic conclusions based on observation and conclusions. mathematical judgment. • Recognize effective transitions between ideas, sentences, • Formulate geometric conclusions based on observation and and paragraphs. mathematical judgment. • Recognize effective and logical organization and • Recognize patterns, logic problems, and geometric organizational strategies. representation of real-life situations.

Purpose, Audience, and Focus Analysis The student will be able to: The student will be able to: • Recognize the role of the audience within varying contexts • Interpret algebraic representations, including those in and draw logical conclusions about the intended audience real-life situations. for a given passage. • Interpret geometric representations, including applying • Understand how the purpose for and focus of a piece of properties in coordinate geometry. writing help determine the kind of information included and • Evaluate statistical arguments, including counting the appropriate style and tone of the piece. principles, measures of central tendency, and interpretation of probabilities. Supporting Details The student will be able to: • Draw conclusions based on supporting details in a passage. • Determine the stated or implied purpose of supporting details within the context of a passage. • Make judgments about the relative importance of supporting details to the passage as a whole.

Style and Craft The student will be able to: • Identify rhetorical features that contribute to the overall precision and style of a piece of writing. • Identify the author’s tone or voice in a piece of writing.

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MATHEMATICS (PART 1 AND 2) • Apply concepts of measure, including perimeter, circumference, surface area, volume, weight, angle measure, The four content strands in the Level 9 Mathematics test are: 1) distance, and slope as they relate to parallel or Numbers and Number Relationships; 2) Geometry and Spatial perpendicular lines. Sense; 3) Data Analysis, Probability, and Statistics; and 4) • Apply concepts of congruence, similarity, and simple Algebra. Level 9 is the first level that has an Algebra content transformation. strand, and the number of questions in Geometry at this level is significantly greater than the number at any prior level. Data Analysis, Statistics, and Probability Additionally, topics included in Level 9 but not in Level 8 are: The student will be able to: • Applying the different forms of real numbers, including • Generate, organize, evaluate, and interpret various data radicals, in a variety of situations. representations, including graphs, charts, and histograms. • Performing operations with different forms of real numbers. • Understand counting techniques for solving problems, • Understanding properties of quadrilaterals, triangles, and including the use of permutations and combinations; circles and applying basic theorems related to them. understand and compute mean, median, mode, and range; and make conjectures and inferences from data provided. • Solving a literal equation for a variable. • Determine probabilities, solve problems of chance using • Applying variables, expressions, and equations to solve ratios and related probabilities, and make predictions based problems. on mathematical probabilities. • Understanding the concepts of slope and x- and y-intercepts, and applying these concepts to finding the equation of a Algebra line, making predictions, and to solving rate problems. The student will be able to: • Represent patterns and mathematical situations using Along with subscores in the content strands, students will tables, graphs, verbal rules, and equations. receive subscores in three process areas: Conceptual Understanding, Procedural Knowledge, and Problem Solving. • Understand properties of operations, including In addition, students receive a subscore in Mathematics commutative and associative, and simplify algebraic Communication if they take the constructed-response expressions. component of the achievement test (available for CTP 4 only). • Solve linear equations and inequalities in one variable and The following is a list of the skills measured by the CTP solve literal equations for a variable. Mathematics test at Level 9. • Apply variables, expressions, and equations to solve Numbers and Number Relationships real-world problems and mathematical problems including The student will be able to: nonlinear equations. • Understand different forms of real numbers and the • Understand slope and x- and y-intercepts and apply these relationships between them including fractions, decimals, concepts to find an equation of a line, make predictions, and percents, and exponential and scientific notation. solve rate problems.

• Understand properties of operations and perform operations Math Communication with different forms of real numbers. Optional Constructed-Response Section • Apply different forms of real numbers in a variety of The constructed-response component of the Mathematics tests situations (forms include radicals). assesses students’ ability to communicate in mathematics. At • Apply theories of whole numbers in a variety of situations. this level, the work students will be able to do includes: showing the solution of a system of equations, explaining Geometry and Spatial Sense properties of parallel lines used to find angle measures, and The student will be able to: using formulas to compute geometric measures.

• Use basic geometric language to classify and characterize * Available for CTP 4 only. properties of geometric figures including quadrilaterals, triangles, circles, and three-dimensional figures. • Apply geometric properties and relationships to two- and three- dimensional figures, including the Pythagorean Theorem, sum of angle measures in a polygon, and triangle inequality; develop formulas to solve geometric problems; and use number line and coordinate geometry.

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ALGEBRA I

The Algebra I test is an end-of-course test and should be administered at the completion of a first-year course in Algebra. The four content strands in the Algebra I test are: 1) Expressions, Statements, and Matrices; 2) Equations and Inequalities; 3) Tables, Graphs, and Algebraic Geometry; and 4) Situations Involving Variable Quantities. The following is a list of the skills measured by the CTP Algebra I test at Level 9.

Expressions, Statements, and Matrices The student will be able to: • Simplify algebraic expressions in various forms by applying arithmetic properties (forms include rational and exponential expressions). • Understand equivalent algebraic expressions, including expressions that are obtained by factoring. • Evaluate algebraic expressions for given values.

Equations and Inequalities The student will be able to: • Solve linear equations/inequalities, simple systems of linear equations, and literal equations for one variable. • Identify arithmetic properties. • Apply algebraic equations to solve real-life problems and mathematical situations. • Solve simple quadratic equations. • Understand relationships of coefficients for equivalent quadratic expressions.

Tables, Graphs, and Algebraic Geometry The student will be able to: • Understand the xy-coordinate system and graphs of points, linear equations, and linear inequalities. • Identify linear equations and their characteristics, including slope and x- and y-intercepts. • Recognize relationships between parallel and perpendicular lines.

Situations Involving Variable Quantities The student will be able to translate real-life and mathematical situations into algebraic expressions or equations.

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VERBAL REASONING Application The student will be able to: The CTP Verbal Reasoning test at Level 10 measures students’ • Identify the correct definition of a word in the context of a ability to conceptualize relationships among words and passage. concepts and to draw conclusions based on incomplete • Identify a synonym or antonym of a word in the context of a information. The ability to infer information that is not passage. explicitly stated in a text is an essential aspect of fluency in reading; the CTP Verbal Reasoning test at Level 10 evaluates students’ developing proficiency in this area. The following is a list of the skills measured by the CTP Verbal Reasoning test at READING COMPREHENSION Level 10. The CTP Reading Comprehension test at Level 10 measures students’ ability to understand and interpret written text. The Analogical Reasoning NCTE/IRA Standards for the English Language Arts emphasizes The student will be able to: the importance of being able to use a “wide range of strategies • Recognize the relationship between two words and identify to comprehend, interpret, evaluate, and appreciate text” (31). another pair of words with the same relationship. The CTP Reading Comprehension test requires students to • Identify the definition that accurately describes the draw on these strategies to interpret and analyze a range of relationship between a pair of words. texts, both fiction and nonfiction. The following is a list of the skills measured by the CTP Reading Categorical Reasoning Comprehension test at Level 10. The student will be able to: Explicit Information • Recognize which of several elements does or does not fit into The student will be able to: a thematically grouped list of words. • Use explicit information to identify the main idea or primary • Generalize about a thematically grouped list of words and purpose of a text or part of a text. choose an appropriate heading for the list. • Identify explicit details from a passage and provide answers Logical Reasoning to “who,” “what,”“where,”“when,”“why,” and “how” The student will be able to: questions about the text. • Solve deductive ordering problems and draw conclusions • Understand connections between and among explicit pieces that are directly deducible from the information provided. of information from a passage. • Solve inductive reasoning problems by reasoning from • Put pieces of information from the passage in correct details or evidence to a generalization or hypothesis that chronological order. makes sense of the evidence. Inference The student will be able to: VOCABULARY • Use implicit information from a passage to make inferences about the motives or behaviors of characters. Reading fluency depends on both an extensive learned • Use implicit information from a passage to answer specific vocabulary and the ability to decode unfamiliar words. The questions about a text. CTP Vocabulary test at Level 10 measures students’ expanding vocabulary and their developing ability to distinguish more Analysis subtle differences among related words. At Level 10, The student will be able to: vocabulary words are tested both in and out of context. The following is a list of the skills measured by the CTP Vocabulary • Determine whether information included in a passage test at Level 10. consists of fact or opinion. • Use explicit and implicit information to determine the Word Meaning author’s likely intent for writing a passage or for including The student will be able to identify synonyms and antonyms of certain information in a passage. words. • Compare and contrast elements in a text. Precision • Categorize and combine pieces of information in a text. The student will be able to distinguish among subtle shades of • Synthesize explicit and implicit information to make meaning in choosing the appropriate word or words to fill in predictions, draw conclusions, or formulate hypotheses the blank(s) in a sentence. about a text. • Identify the style, tone, or theme of a text.

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• Spelling of commonly used words, including words with READING COMPREHENSION CONTINUED affixes and words that display improper pluralization. Reading for Understanding • Capitalization of proper nouns. Optional Constructed-Response Section* • Capitalization in titles and forms of address. Students use their developing productive language skills to • The correct use of the comma, semicolon, and colon. answer questions about text, employing comprehension strategies to interpret and analyze the texts, describe • The correct use of the apostrophe in contractions and important aspects of the texts, synthesize information from possessives. two texts, and compare and contrast elements within a text • Proper punctuation for dialogue and quotations. and/or between two texts. At level 10, most questions require students to make inferences about information that is not • Correct end punctuation. explicitly stated in the text. At this level, students are also asked to apply their growing understanding of figurative Usage language to answer some questions. The student will be able to: The student will be able to apply rules of English diction and grammar. Specific rules tested include: • Describe the main idea or overall theme of a passage and/or • Correct pronoun use, including pronoun-antecedent summarize the main points of a passage. agreement. • Describe a supporting idea in a passage. • Correct verb form and tense, including subject-verb • Apply understanding of figurative language to describe agreement and parallelism. aspects of a passage. • Rules of correct and effective expression at the sentence • Compare and contrast elements from two texts. level, including proper modification. • Make inferences about a character’s motivation. • Rules of diction within the context of a sentence. • Make inferences about the author’s purpose. • Rules regarding sentence boundaries, including avoiding run-ons and fragments and recognizing sentence types. • Synthesize information from two texts to describe supporting ideas, make predictions, or draw conclusions. WRITING CONCEPTS AND SKILLS NOTE: Although the Reading for Understanding section does require students to write their answers, it is a test of The CTP Writing Concepts and Skills test at Level 10 integrates reading comprehension and not writing ability. Students’ responses are evaluated based on how completely and students’ developing facility with English grammar and usage thoroughly they answer the questions; misspellings, with an increasingly sophisticated understanding of the grammatical mistakes, and other writing errors do not writing process. As students continue to develop their writing count against them. The questions are scored on a 0-2 skills, the ability to organize complex information and to scale. recognize the multiple purposes and audiences for writing becomes increasingly important. According to the NCTE/IRA * Available for CTP 4 only. Standards for the English Language Arts, it is important that students be able to “employ a wide range of strategies as they write and use different writing process elements appropriately WRITING MECHANICS to communicate with different audiences for a variety of purposes” (35). The following is a list of the skills measured by The development of an increasingly sophisticated the CTP Writing Concepts and Skills test at Level 10. understanding of language conventions and mechanics is essential as students continue to write more and more Organization complex texts. The NCTE/IRA Standards for the English The student will be able to: Language Arts indicates that students should be able to “apply • Recognize thesis statements, topic sentences, and knowledge of language structure and language conventions conclusions. (e.g., spelling and punctuation) . . . to create, critique, and discuss print and non-print texts” (36). The CTP Writing • Recognize effective transitions between ideas, sentences, Mechanics test at Level 10 measures students’ growing facility and paragraphs. with English sentence structure and language conventions. • Recognize effective and logical organization in a piece of The following is a list of the skills measured by the writing. CTP Writing Mechanics test at Level 10. • Understand and recognize carious organizational strategies.

Spelling, Capitalization, and Punctuation The student will be able to recognize spelling, capitalization, and punctuation errors. Specific elements tested include:

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Analysis WRITING CONCEPTS AND SKILLS CONTINUED The student will be able to: Purpose, Audience, and Focus • Interpret algebraic representations, including those in The student will be able to: real-life situations. • Recognize the role of the audience within varying contexts and • Interpret geometric representations, including applying draw logical conclusions about the intended audience for a properties in coordinate geometry. given passage. • Evaluate statistical arguments, including counting • Understand how the purpose for and focus of a piece of writing principles, measures of central tendency, and interpretation help determine the kind of information included and the of probabilities. appropriate style and tone of the piece.

Supporting Details MATHEMATICS (PART 1 AND 2) The student will be able to: • Draw conclusions based on supporting details in a passage. The five content strands in the Level 10 Mathematics test are: 1) Numbers and Number Relationships; 2) Geometry and Spatial • Determine the stated or implied purpose of supporting details Sense; 3) Data Analysis, Probability, and Statistics; 4) Algebra; within the context of a passage. and 5) Functions. This is the first level that specifically includes • Make judgments about the relative importance of supporting a content strand in functions. Additionally, topics included in details to the passage as a whole. Level 10 but not in Level 9 are: • Recognize effective and relevant details to support points made • Understanding real and complex numbers. in a piece of writing. • Performing operations with complex numbers.

Style and Craft • Understanding the application of mutually exclusive and The student will be able to: independent events in probabilities. • Identify rhetorical features that contribute to the overall • Solving and graphing second-degree equations and precision and style of a piece of writing. inequalities. • Identify the author’s tone or voice in a piece of writing. • Solving and graphing linear inequalities and solving linear programming problems. • Understanding matrices and performing operations with QUANTITATIVE REASONING matrices. • Understanding conic sections and their relationships, with The Quantitative Reasoning test assesses students’ ability to an emphasis on circles and parabolas. engage, in age-level appropriate ways, in pattern recognition, classification, and reasoning in all content areas, including logic, • Understanding the properties and relationships of rational arithmetic, algebra, geometry, probability, and statistics. exponents. The following is a list of the skills measured by the CTP • Understanding systems of equations and/or inequalities and Quantitative Reasoning test at Level 10. their applications. • Understanding functions and their graphs, including Comparison The student will be able to: domain and range, and operations with functions such as composition. • Consider numerical quantities in various forms and compare their sizes. • Understanding absolute value, logarithmic, and exponential functions. • Consider the relative measures of geometric shapes. • Using functions to represent and interpret real-world applications. Extensions and Generalizations The student will be able to: • Understanding and applying trigonometric functions in • Formulate arithmetic conclusions based on observation and basic right- triangle situations. mathematical judgment. • Using the trigonometric identity sin2 x + cos 2 x = 1 in various • Formulate geometric conclusions based on observation and situations. mathematical judgment. • Recognize patterns, logic problems, and geometric representation of real-life situations.

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Algebra MATHEMATICS CONTINUED The student will be able to: Along with subscores in the content strands, students will • Represent patterns and mathematical situations using receive subscores in three process areas: Conceptual tables, graphs, verbal rules, and equations. Understanding, Procedural Knowledge, and Problem Solving. In addition, students receive a subscore in Mathematics • Understand properties of operations, including Communication if they take the constructed-response commutative and associative, and simplify algebraic component of the achievement test (available for CTP 4 only). rational expressions. The following is a list of the skills measured by the CTP • Solve and graph first- and second-degree equations and Mathematics test at Level 10. inequalities in one variable, solve literal equations for a variable, and understand conic sections and their equations. Numbers and Number Relationships • Understand systems of equations and inequalities and their The student will be able to: applications and understand matrices and perform basic • Understand different forms of complex and real numbers operations with them. and the relationships between them, including rational and • Apply variables, expressions, and equations to solve irrational real numbers and exponential and scientific real-world problems and mathematical problems including notation. nonlinear equations. • Understand properties of operations and perform operations • Understand slope, x- and y-intercepts, and relationships with different forms of real numbers and complex numbers. between parallel and perpendicular lines and apply these • Apply different forms of real numbers in a variety of concepts to find an equation of a line, make predictions, and situations (forms include radicals). solve rate problems. • Apply theories of whole numbers in a variety of situations. Functions Geometry and Spatial Sense The student will be able to: The student will be able to: • Understand properties of functions and their graphs, • Use basic geometric language to classify and characterize including domains and ranges. properties of geometric figures, including quadrilaterals, • Understand the relationships between functions, their triangles, circles, and three- dimensional figures, and apply transformations, and their inverses and apply composition basic theorems to these figures. and other operations with functions. • Apply geometric properties and relationships to two- and • Apply trigonometric functions in right-triangle situations three- dimensional figures, including the Pythagorean and use the fundamental trigonometric identity Theorem, sum of angle measures in a polygon, and triangle sin2 x + cos2 x = 1. inequality; develop formulas to solve geometric problems; • Understand absolute value, logarithmic and exponential and use number line and coordinate geometry. functions, and their applications to real-world problems, • Apply concepts of measure, including perimeter, including exponential growth and decay and predictions of circumference, surface area, volume, weight, angle measure, business trends. distance, and slope as they relate to parallel or perpendicular lines. Math Communication • Apply concepts of congruence, similarity, and simple Optional Constructed-Response Section* transformation. The constructed-response component of the Mathematics tests assesses students’ ability to communicate in mathematics. At Data Analysis, Statistics, and Probability this level, the work students will be able to do includes: The student will be able to: evaluating data using standard deviation, using properties of • Generate, organize, evaluate, and interpret various data similar triangles, sketching the graph of a quadratic equation, representations, including graphs, charts, and histograms. and using triangle inequality and special triangles to find lengths of sides. • Understand counting techniques for solving problems, including the use of permutations and combinations; * Available for CTP 4 only. understand and compute mean, median, mode, range, and standard deviation; and make conjectures or inferences from data provided. • Determine probabilities, solve problems of chance using ratios and related probabilities, and make predictions based on mathematical probabilities and apply probabilities to mutually exclusive and independent events.

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AUDITORY COMPREHENSION READING COMPREHENSION (Material read aloud to students is indicated in italics.)

Sample Questions 3-5 are based on the following passage. Sample Question 1: It was time for art class. Miss Wang said, “Clear the papers from your tables. Then take out a pencil, Puddles the Duck did not like to be dry. scissors, and two markers.” He liked to be wet.“ Where can I Which picture shows what should be on the table? splash?” said Puddles. Puddles looked for a wet place. All of the places that once were wet, now were dry. (A) (B) “ Where can I find water?” he asked. He went to find Cow.“ Hi, Cow,” said Puddles.“ I am looking for water.” “ It has been very dry. But there is water by the barn,” said (C) (D) the cow.“ Farmer Dodd put a tub of water there.” “ Oh, boy!” cried Puddles.“ Water!” Away ran Puddles.

Content Category: Explicit Information / Detail This question asks students to recognize what each student in Miss Wang’s class should have on his or her table after Sample Question 3: What does cried mean in the story? following the teacher’s directions. T he teacher told the students to “take out a pencil, scissors, and two markers.” The (A) Yelled correct answer, therefore, is (B). (B) Looked (C) Sobbed (D) Splashed Sample Question 2: What did Miss Wang ask the class to do before they got out their art supplies? Content Category: Vocabulary in Context This question asks students to recognize the meaning of the Put on their Take out some Clear off their Take out some word “ cried” as it is used in the story. While one meaning of art smocks markers tables paper crying is to “ sob,” nothing in the passage indicates that (A) (B) (C) (D) Puddles is sad; therefore, (C) can be eliminated. In the story, Puddles cried “ Oh, boy!” and “ Water!” The use of the Content Category: Explicit Information / Detail exclamation marks in these comments and Puddles’ running In this question, students are expected to recognize what Miss indicate his excitement. Puddles most likely “ yelled” these Wang’s students were first instructed to do in preparation for comments. Therefore, (A) is the correct answer. the art class. Miss Wang told the students first to “clear the papers from [their] tables” and then to take out their art supplies (pencil, scissors, and two markers). Therefore, the correct answer is (C). Sample Question 4: What is the best title for this story? (A) The Duck Who Liked to Be Dry (B) Fun in the Barn (C) Farmer Dodd’s Cow (D) Puddles the Duck

Content Category: Inference / Summarize The question asks for the best title to this story. Option (A) can be eliminated because it contradicts the story, which indicates that Puddles would rather be wet than dry. Option (B) can easily be eliminated, since having fun in the barn is not mentioned in the story. Choice (C) is more plausible, since Cow is mentioned in the story; however, the story’s main focus is not on Cow. The story is about Puddles. Therefore, (D) is the best answer.

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READING COMPREHENSION CONTINUED Sample Question 6: What can make this plane move through the air? (A) The pilot (B) Batteries Sample Question 5: What will Puddles do next? (C) Jet engines (A) Run to the puddle (D) The person playing with it (B) Run to the tub of water (C) Ask Cow where to find water Content Category: Inference / Draw Conclusions (D) Ask Farmer Dodd to get some water The question asks students to recognize how this toy plane moves through the air. Choice (A) might appeal because Content Category: Analysis / Prediction “pilots” do fly planes; however, this is a toy that must be In the story, Puddles is looking for water, and Cow tells him operated by a person. Options (B) and (C) are also likely to that there is a tub of water by the barn. The question asks appeal, but they too are incorrect; the batteries supply the students to predict what Puddles is likely to do next. Puddles’ sounds of the jet engines. The correct answer is (D). According excitement at Cow’s response clearly indicates that Puddles is to the ad “ you can make this plane do loops, dips, and big headed for the water Cow described. The correct answer, circles by moving it through the air.” therefore, is (B).

Sample Question 7: Why is this ad in the paper? Sample Questions 6 and 7 are based on the following (A) So you will have fun passage. (B) So you will buy batteries (C) So you will buy this toy plane (D) So you will tell your friends

Content Category: Analysis / Make Connections In this question, students are expected to understand the primary reason for this ad being in the newspaper. While having fun (A) and buying batteries (B) might result from owning the plane, and telling your friends about the plane (D) might make more people want to buy it, the description of the toy plane and the mention of its cost clearly indicate that the primary purpose of this ad is to get the reader to buy the plane. Be the first to have a new This purpose is reinforced by the closing statements “ Hurry!”“ Supplies limited!”“ At a toy store near you!” Therefore, (C) is the STAR WING SUPERSONIC PLANE correct answer. This toy is made of tough plastic painted with flames that look real. It comes with a pilot and his own parachute.

Includes small map and compass.

You can make this plane do loops, dips, and big circles by moving it through the air.

Real flying sounds like sirens and the roar of jet engines. Batteries not included.

The Plane is 12 inches across and 5 inches high.

ONLY $15.00 Hurry! Supplies limited! At a toy store near you!

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READING COMPREHENSION Sample Question 8: Name the tricks that the sea lions did Optional Constructed-Response Questions (CTP 4 Only) at the circus. Include at least three examples in your response.

Content Category: Reading for Understanding In order to receive a 2 (the highest score) on this question, the student must show clear and solid understanding of the tricks that the sea lions did at the circus. The response must include at least three of the following tricks: • Played music/played horns. • Clapped. • Played catch/threw ball. • Climbed ladder. • Went down the slide. • Splashed people. A score of 1 indicates that a student shows basic (but in some way incomplete) understanding of the tricks that the sea lions did at the circus; the response must include one or two of the Read Passage 1 to find out about a boy who sees sea tricks listed above. lions at the circus. A score of 0 indicates that a student shows very little or no Sea Lions at the Circus understanding of the tricks that the sea lions did at the circus; The circus was here! Ramon and his dad got there early. a response in this category mentions none of the tricks listed They found good seats in the front row with excellent above or gives only incorrect information. views. They wanted to see the sea lions. They laughed as the sea lions waddled into the circus ring. They all looked so clumsy. Their trainer held up a horn to their mouths and the sea lions played music. Ramon and his dad clapped. Then the sea lions clapped their flippers together. That made Ramon and his dad clap even more. The trainer threw a beach ball to the first sea lion. That sea lion threw it to another one. Soon all the sea lions were playing catch. Every time the sea lions did a trick, the trainer threw a fish treat to them. At the end of the show, the sea lions climbed up a ladder and shot down the slide. When they hit the water, Ramon and his dad got splashed. They got very wet and cold, but they knew they would dry off soon. They clapped and clapped. The sea lions clapped too. Maybe some day Ramon and his dad can watch the sea lions in the water where they live. In the circus ring, the sea lions look funny and make us laugh. But in the sea they are fast and graceful.

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READING COMPREHENSION CONTINUED Sample Question 9: These two stories tell how sea lions Optional Constructed-Response Questions (CTP 4 Only) are different at the circus and in the sea. Fill in this chart to show how they are different in those two places.

Sea Lions at the Circus Sea Lions in the Sea This is what the sea lions eat at This is what the sea lions eat in the circus: the sea:

This is how the sea lions move This is how the sea lions move at the circus: in the sea:

Read Passage 2 to learn about how sea lions live in the sea. Sea Lions in the Sea This is how the sea lions get This is how the sea lions get People like to watch the sea lions at the circus. The sea their food at the circus: their food in the sea: lions look funny as they drag their large, heavy bodies around the ring. We laugh at them because they look really clumsy. The best place to watch the sea lions is in the sea, not on dry land. At home in the water, they swim fast and they are graceful. Content Category: Reading for Understanding To get their food, sea lions must chase fish. The fish swish In order to receive a 2 (the highest score) on this question, the back and forth, hoping they will not get caught. But the student must show clear and solid understanding of how sea sea lions follow them at great speed. They twist and turn lions are different at the circus and in the sea. The student must their necks close behind the fish. The sea lions are even fill in each of five or six cells with at least one correct response, faster than the fish. One sea lion can catch up to 40 as indicated by the following list. pounds of fish every day. • Sea Lions at the Circus Sea lions have their babies in the spring. A baby sea lion What they eat: fish/fish treats. stays with its mother for about a year. The mother will How they move: clumsy/funny/drag their bodies/waddle. keep it safe. Mothers will also make sure their babies have How they get their food: from doing tricks/from the trainer. plenty to eat. The babies spend their time eating and growing. They eat fish, octopus, and seabirds. • Sea Lions in the Sea What they eat: fish/octopus/seabirds/40 pounds of fish. How they move: fast/graceful. How they get their food: catch fish.

A score of 1 indicates that the student shows basic (but in some way incomplete) understanding of how sea lions are different at the circus and in the sea; the student must fill in three or four cells with at least one correct response (as indicated by the list above). A score of 0 indicates that the student shows very little or no understanding of how sea lions are different at the circus and in the sea. To receive a score of 0, the student must have filled in only one or two of the above cells with a correct response or given only incorrect information.

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WORD ANALYSIS WRITING MECHANICS (Material read aloud to students is indicated in italics.)

For Sample Questions 13 and 14, find the word that goes in Sample Question 10: Look at the four underlined words in the blank to make the sentence correct. the sentence. Fill in the bubble under the one that is a compound word. Sample Question 13: going to take a long time to fix the car. The children may not use the school playground when it is raining. Its’ It It’s Its (A) (B) (C) (D) (A) (B) (C) (D)

Content Category: Structural Analysis / Compound Words Content Category: Punctuation / Apostrophe In this question, students are to select the choice that is a In≠ this question, students are being tested on the difference compound word. (C) is the correct answer because it is the only between “ its,” meaning “ belonging to it” and “ it’s,” meaning “ word made up of two independent words with distinctive it is.” In this sentence, the blank represents a missing subject meanings. and verb; therefore, the correct answer is (C).

Sample Question 11: Which word has the same vowel Sample Question 14: Most little sound as the word seem? puppies.

top seat wet shoe kid like kids like kids likes kid likes (A) (B) (C) (D) (A) (B) (C) (D)

Content Category: Phonemic Analysis / Medial Vowel Content Category: Usage / Verb Form and Tense Sounds The question asks students which word has the same This question asks students to select the choice that reflects vowel sound as the word seem. Recognition of the long e sound correct subject-verb usage, thereby making the sentence is being tested. “Seat” is most similar in sound to the word correct. The use of the word “ Most” indicates that the subject “seem” ; therefore, (B) is the correct answer. of this sentence will be plural; therefore, the correct answer must have a plural subject with a corresponding plural verb. Option (A) is incorrect because the subject is singular and also because the verb form is plural; subject and verb must agree in Sample Question 12: Which word ends with the same number. Option (D), though correct in subject-verb agreement, sound as the word band? is still wrong, since the subject is again singular, and option (C), with its plural subject, is incorrect because the verb is sing long any wind singular. Option (B) is therefore the correct answer. (A) (B) (C) (D)

Content Category: Phonemic Analysis / Final Consonant Sounds This question asks students to recognize which word ends with the same sound as the word band. “Wind,” (D), and “band” end in the same sound, the consonant blend “nd.” Therefore, (D) is the correct answer.

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MATHEMATICS Sample Question 18: A class of 13 boys and 16 girls went (Material read aloud to students is indicated in italics.) on a field trip. Two teachers also went on the field trip. Which number sentence can be used to find how many people went on the field trip?

Sample Question 15: There were 58 children on the 13 + 16 + 2 = 13 + 16 - = 31 13 - 16 + 2 = 13 + 16 + = 29 playground outside. After recess, 27 went back inside. How (A) (B) (C) (D) many were still on the playground outside? Content Category: Patterns, Functions, and Pre-Algebra / 31 35 49 85 Conceptual Understanding The problem asks for a number (A) (B) (C) (D) sentence that can be used to find the total number of people that went on the field trip. This total number is the sum of the numbers of boys, girls, and teachers that went on the field trip. Content Category: Number Sense and Operations with Since 13 boys, 16 girls, and 2 teachers went on the field trip, the Whole Numbers / Problem Solving There were initially 58 correct number sentence requires the expression 13 + 16 + 2. children on the playground outside, and 27 children went back The correct answer is choice (A). inside after recess. The number of children that were still on the playground outside is given by the difference 58 – 27. This difference is 31. The correct answer is choice (A).

Sample Question 16: How many triangles are in the picture?

2 3 4 5 (A) (B) (C) (D)

Content Category: Geometry and Spatial Sense / Problem Solving To solve this problem, notice that there are four smaller triangles inside of one larger triangle. Therefore, the total number of triangles in the picture is 5. The correct answer is choice (D).

Sample Question 17: How many of the shapes have only straight edges?

1 2 3 4 (A) (B) (C) (D)

Content Category: Geometry and Spatial Sense / Conceptual Understanding The only shapes that contain only straight sides are the rectangle, the triangle, and the star. There are 3 shapes having only straight sides. The correct answer, therefore, is choice (C).

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MATHEMATICS Optional Constructed-Response Questions (CTP 4 Only)

Sample Question 19: A pattern of buttons is shown below. Draw the next 3 buttons in the pattern.

Content Category: Math Communication Notice that the button pattern contains two characteristics – button size and the number of button holes. The button size alternates back and forth between small and large. The number of button holes alternates back and forth between two holes and four holes. The next three buttons in the pattern should therefore be a large button with four holes, followed by a small button with two holes, followed by a large button with four holes. To score a 1 on this question, students could show an understanding of this pattern but start with the incorrect button. Another way students can score a 1 on this question is to have only the number of button holes correct or only the button size correct in their pattern.

Sample Question 20: For each number below, write the number that is 1 more, 10 more, and 100 more on the blank line. The first number is done for you as an example.

1 more 10 more 100 more 5 6 15 105 109 489 2,699 30,500

Content Category: Math Communication To solve this problem, each number in the left-hand column is to be added to 1, 10, and 100, respectively. The correct answers for each row are given below. To score a 1 on this question, a student must fill in 2 or 3 rows completely correctly.

1 more 10 more 100 more 5 6 15 105 109 110 119 209 489 490 499 589 2,699 2,700 2,709 2,799 30,500 30,501 30,510 30,600

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VERBAL REASONING AUDITORY COMPREHENSION (Material read aloud to students is indicated in italics.)

Sample Question 1: Which lettered pair of words goes together in the same way as the first pair of words? Listen very carefully while I tell you a story from China that is very much like “Little Red Riding Hood.” SNIFF : SMELL :: (A) glance : look Once, long ago, there was a woman who lived alone in the (B) seek : find country with her three children — Shang, Tao, and Paotze. On (C) talk : gossip the day of their grandmother’s birthday, the good mother set off (D) buy : sell to see her, leaving the three children at home.

Content Category: Analogical Reasoning Before she left, she said,“Be good while I am away, my heart- The correct answer to this reasoning problem is (A). The two loving children; I will not return tonight. Remember to close the terms in the original pair are related by degree: to sniff is to door tight at sunset and latch it well.” smell quickly. Only the pair of words in option (A) has an But an old wolf lived nearby and saw the good mother leave. At analogous relationship: to glance is to look quickly. dusk, disguised as an old woman, he came up to the house of the children and knocked on the door twice: bang, bang. Shang, who was the eldest, said through the latched door,“Who is it?” “My little jewels,” said the wolf,“this is your grandmother, Sample Question 2: Jamal and Alison have made up their your Po Po.” “Po Po!” Shang said.“Our mother has gone to visit own language. In this language, tiff lam means “they are,” bon you!” lam means “we are,” and bon sen means “we will.” (A) Tiff sen (B) Tiff bon (C) Bon bon Sample Question 3: What does the word latch mean in the (D) Bon tiff story?

Content Category: Logical Reasoning / Inductive Reasoning Close Lock Bang Guard To answer this question, the student must determine which (A) (B) (C) (D) words defined in the problem mean they and will. Since tiff lam means they are and bon lam means we are, lam must Content Category: Vocabulary in Context mean are and tiff must therefore mean they. Knowing only that This question asks students to determine the meaning of the tiff lam means they are would not provide enough information word “latch” in the context of the story. “Latch” means to shut to determine which word means they, because it is not tightly so that a latch is engaged. Option (A) is appealing but necessarily the case that word order in Jamal and Alison’s not accurate, since closing a door does not mean fastening it language follows the same rules as English. Using similar rules with a latch. Only (B) involves fastening the door, so option (B) of induction, it can be determined that sen means will. The is the correct answer. correct answer is (A).

Sample Question 4: Where did the “good mother” go?

To the To the wolf’s To visit the To latch the market house grandmother door (A) (B) (C) (D)

Content Category: Explicit Information / Detail The question asks the students to recall an important detail of the plot of the story. Only (C) is an accurate account of where the “good mother” went, so option (C) is the correct answer.

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AUDITORY COMPREHENSION CONTINUED READING COMPREHENSION (Material read aloud to students is indicated in italics.)

Sample Questions 6 - 9 are based on the following passage. Sample Question 5: Why did the wolf disguise himself as

an old woman?

He wanted to He did not like He wanted to talk to the the way his fur fool the The mother grandmother. looked. children. might see him. (A) (B) (C) (D)

Content Category: Inference / Motives and Behaviors Why Are Some Fish Flat? This reasoning question asks students to infer from the story the Flatfish, such as flounder or sole, hatch from eggs like wolf ’s reason for disguising himself as an old woman. The only other fish. They hatch near the surface of the sea and start option that offers a likely explanation for the wolf ’s behavior is life with a normal fish shape. But when they are just a few (C): the wolf disguised himself to fool the children. The other weeks old, their shape begins to evolve. options don’t make logical sense and/or are not supported by the details in the story. First of all, one eye moves around to the other side of the fish’s head so that both eyes are on the same side. Then the fish swims down to lie on the seabed. It lies on its blind side with both its eyes staring upward. Then gradually, the fish’s body flattens out. Instead of a right and a left side, a flatfish has a top and a bottom side. Flatfish spend most of their lives lying on the seabed. Their shape helps them hide from enemies and catch food more easily. Their top sides are often the same color as the seabed, so that they can take prey by surprise.

Sample Question 6: What is the main idea of the passage? (A) Flounder and sole are specific kinds of flatfish found in the ocean. (B) Flatfish have special features that make them different from other fish. (C) Flatfish have both eyes on the same side of their body. (D) The shape of flatfish helps them catch prey.

Content Category: Explicit Information / Main Idea This question asks students to recognize the main idea of the passage, as opposed to a secondary or supporting idea. All of the options are points made in the passage, but only (B) states the main idea of the passage: flatfish have unique features that distinguish them from other fish.

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READING COMPREHENSION CONTINUED

Sample Question 7: What enables flatfish to take their prey by surprise? (A) Their color is the same as the seabed. (B) Both eyes are on the same side of the fish. (C) They can swim very fast. (D) Their body is flat.

Content Category: Explicit Information / Detail This question asks students to determine which characteristic of flatfish enables them to take their prey by surprise. The student must recall information provided in the end of the passage: a fish can blend in with the seabed and therefore surprise its prey. Option (A), which specifically addresses this point, is the correct answer. Option (D) is appealing, but while the passage indicates that the fish’s flat shape helps it “catch food more easily,” it does not specifically state that the fish’s shape helps it take prey by surprise. Therefore, (A) is the best answer.

Sample Question 8: The author probably wrote this passage to: (A) Convince people to eat flatfish. (B) Teach people how to catch flatfish. (C) Teach people about flatfish. (D) Warn people about flatfish.

Content Category: Inference / Motives and Behaviors This question asks students to infer from the passage the author’s purpose in writing the passage. Only (C) offers a likely purpose, given the content of the passage, which is a discussion about the distinctive features of flatfish. Therefore, (C) is the correct answer.

Sample Question 9: Flatfish are different from most other fish in all of the following ways EXCEPT: (A) Flatfish have both eyes on the same side of their body. (B) Flatfish have a top and bottom instead of a right and left side. (C) Flatfish lay eggs in the water. (D) Flatfish spend most of their lives lying on the seabed.

Content Category: Analysis / Draw Conclusions The student must perform two different tasks to determine the answer to this question. First, the student must decide which option is a characteristic that is NOT unique to flatfish. Options (A), (B), and (D) all describe characteristics that ARE unique to flatfish. Second, the student must infer from the passage that flatfish lay eggs in the water, since the passage indicates that flatfish “hatch from eggs like other fish.” The correct answer, then, is option (C).

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READING COMPREHENSION Sample Question 10: According to Passage 1, where are Optional Constructed-Response Questions (CTP 4 Only) three places where you might find pictures of eagles?

Content Category: Reading for Understanding In order to receive a 2 (the highest score) on this question, the Sample Question 10 is based on the following passage. student must show clear and solid understanding of three places where one might find pictures of eagles; the student’s response must include three of the following. • Great Seal (of the United States) • Presidential seal • Paper money • Coins • Mascot (for sports team) To receive a score of 1, the student must show basic (but in some way incomplete) understanding of places where one might find pictures of eagles; the student’s response must include one or two of the above.

A score of 0 indicates that the student shows very little or no Read Passage 1 to learn more about eagles. understanding of places where one might find pictures of eagles; The eagle is a beautiful bird. It is one of the largest birds in a response in this category mentions none of the places listed the world. The bald eagle is the national symbol of the above or gives only incorrect information. United States. But it is not bald at all. It is called the bald eagle because the feathers on its head and neck are pure white. Eagles have large, strong beaks. The beak is very sharp and pointed. The top half of the beak curves down over the bottom half. Eagles are good hunters. They have large, powerful claws. They can swoop down out of the sky to catch a small animal like a mouse or even a fish. Many people think the eagle is a sign of strength and bravery. It is also a symbol of freedom. The picture of the eagle is on the Great Seal of the United States and also on the President’s seal. You can also find a picture of an eagle on some U.S. coins and paper money. When people think of eagles, they think of power, courage, and skill. Because of this, many groups use the eagle as their symbol. Some sports teams use the eagle as their mascot. They call their team The Eagles. They want people to think their players are strong and brave.

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READING COMPREHENSION CONTINUED Sample Question 11: According to what you read in Optional Constructed-Response Questions (CTP 4 Only) Passage 1 about why some people choose the eagle as a symbol or mascot, how do you think the Eastside students want people to think of their school? Give at least two examples.

Sample Question 11 is based on the following passage. Content Category: Reading for Understanding In order to receive a 2 (the highest score) on this question, the student must show clear and solid understanding of what the choice of an eagle as school symbol indicates about how the Read Passage 2 to learn what the students at Eastside Eastside students want people to think of their school; the Elementary School voted for. student’s response must include two of the following. The students at Eastside Elementary School wanted to have a new school symbol. The principal told the students • Powerful/strong that many schools choose an animal as a school symbol. • Courageous/brave A school’s symbol is also called a mascot. This is what the • Skillful principal said the mascot should be. • Beautiful • Free • It should be something that is special to the students. • Representing the United States • It should be something that makes them feel proud. • It should be fun. In order to receive a score of 1, the student must show basic (but in some way incomplete) understanding of what the choice of an The students talked about what they wanted their school eagle as school symbol indicates about how the Eastside mascot to be. Mallory said she thought the eagle would be students want people to think of their school; the student’s a good symbol for their school. Here are some reasons response must include one of the examples listed above. that Mallory gave. A score of 0 indicates that the student shows very little or no • We could be called the Eastside Eagles. The name has a understanding of what the choice of an eagle as school symbol nice sound to it. indicates about how the Eastside students want people to think • We can get an eagle costume and have someone wear of their school; a response in this category mentions none of the it at our school events. examples listed above or gives only incorrect information. • We can put the symbol on our school flag. • The eagle will make a nice design.

The Eastside students voted on their school mascot. They also had a contest to have someone draw the school symbol. This is the symbol they chose. It was drawn by Maria.

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WRITING MECHANICS WRITING CONCEPTS AND SKILLS

Sample Question 12: Find the capitalization error in the Sample Question 14: Choose the opening sentence that sentence, if there is one. goes best with the details in the paragraph. . When they arrive there, the females give Many students at Rosewood Elementary School speak russian. birth in the warm lagoons. They journey back in summer to the (A) (B) (C) cold waters of the Arctic. No error (D) (A) Gray whales push water out of their mouths. (B) Gray whales feed by swimming on their sides. Content Category: Capitalization / Proper Noun (C) Some whales live in the North Atlantic. This question asks students to identify a capitalization error. (D) Gray whales travel in the winter to warm water. Since the names of groups of people and their languages should be capitalized, the lowercase “r” in “russian” is Content Category: Organization / Topic Sentences incorrect. Therefore, (C) is the correct answer. This question asks students to choose the topic sentence that is best supported by the details provided in the rest of the paragraph. The paragraph describes female whales traveling to warm lagoons to give birth and then returning to cold waters in Sample Question 13: Find the punctuation error in the the summer. Only option (D) refers to whales traveling in winter sentence, if there is one. to warm water, so (D) is the correct answer.

Mr. Lee , the art teacher , is having the students create a mural. (A) (B) “I want to draw a dolphin,” remarked Sarah. “They’re the best ! ” Sample Question 15: Which topic would be best to use in (C) a report about learning to swim? No error (A) What creatures cannot live in salt water. (D) (B) Fun at a pool party. (C) How to hold your breath while swimming under water. Content Category: Punctuation (D) The need for fences around pools. This question asks students to recognize the correct use of commas and end punctuation. Since all of the underlined Content Category: Purpose, Audience, and Focus / Relevant punctuation marks are correct, the answer is (D), or No error. Information This question asks students to choose an appropriate topic for discussion in a report about learning to swim. Only (C), which describes a skill important in learning to swim, is relevant to this topic, so option (C) is the correct answer.

Sample Question 16: The sentence at the beginning of the question is the main idea of a paragraph. Decide which of the choices goes best with the main idea. Snails prefer dark and moist areas. (A) Snails move slowly. (B) Snails spend time in shells. (C) Snails crawl on rainy nights. (D) Snails eat plants.

Content Category: Supporting Details / Relevant This question asks students to select the option that supports the statement “Snails prefer dark and moist areas” with appropriate details. Since (C) is the only option that refers to places that are both dark and moist (“Snails crawl on rainy nights”), option (C) is the correct answer.

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WRITING CONCEPTS AND SKILLS QUANTITATIVE REASONING CONTINUED

Sample Question 17: Choose the best way of stating the idea. (A) Jean planted flowers that were hers and watered her flowers. Figure A Figure B (B) Jean planted and watered her flowers. The number of The number of (C) Jean watered her flowers and planted them. triangles in rectangles in (D) Jean planted and Jean watered her flowers. Figure A Figure B

Content Category: Style and Craft / Sentence Construction A B This question asks students to determine which statement is the most sensible and concise. Options (A), (C), and (D) are either illogical or unnecessarily wordy. (B) is the only option that makes a sensible and concise statement: Jean planted and watered her flowers. Sample Question 18: Which statement is true? (A) A is greater than B. (B) B is greater than A. (C) A and B are equal.

Content Category: Comparison This is a quantitative comparison question in which students are asked to compare the number of shapes contained in two figures. Figure A contains 5 triangles. There are 3 large triangles that overlap. There are also 2 smaller triangles formed by the large overlapping triangles. Figure B contains 5 rectangles. There are 3 different-sized rectangles shown. There are also 2 larger rectangles that consist of 2 of the smaller rectangles. So, the number in column A is the same as the number in column B. The correct answer is choice (C).

Sample Question 19: Which number would NOT appear in the pattern 4, 8, 12, 16, . . . ? (A) 20 (B) 32 (C) 50 (D) 100

Content Category: Extensions / Generalizations The pattern formed by the numbers shown must be recognized. Each number in the pattern is a multiple of 4. Of the answer choices only one is NOT a multiple of 4. The only choice that is not a multiple of 4 is 50. The correct answer is choice (C).

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MATHEMATICS Sample Question 22: How many boxes of oranges can be bought with $35.00 ? (A) Six (B) Seven Sample Question 20: How many of the numbers from 1 to (C) Eight 20 are odd? (D) Nine (A) 7 (B) 8 Content Category: Number Sense and Operations with (C) 10 Fractions and Decimals / Problem Solving Each box of (D) 11 oranges costs $4.00. To find out the number of boxes of oranges that can be bought with $35.00, divide Content Category: Number Sense and Operations with 35 by 4. Whole Numbers / Conceptual Understanding 8R3 There are 20 numbers from 1 through 20. Half of the numbers 4)35 are even and half of them are odd. Therefore, there are 10 odd numbers from 1 to 20. The correct answer is choice (C). Since the answer is 8R3, 8 boxes can be bought with $35.00. Eight boxes of oranges cost 8 times $4.00 or $32. Nine boxes cost 9 times $4.00 or $36, which is over the $35.00. Therefore, 8 boxes can be bought with $35.00. The correct Sample Questions 21 and 22 refer to the following answer is choice (C). information.

Sample Question 23: Which of these could be the height of a stop sign? (A) 2 meters (B) 6 meters Watermelon 83¢ per pound Oranges $4.00 per box (C) 800 centimeters (D) 1,000 centimeters

Content Category: Measurement / Conceptual Sample Question 21: How much does a 7-pound Understanding The height of a stop sign must be estimated. watermelon cost? Most stop signs are a little taller than an average adult. So you (A) $5.61 can estimate that a stop sign is between 6 and 8 feet tall. Of the (B) $5.71 answer choices, only one is close to this height. The first two (C) $5.74 choices are in meters. One meter is a little longer than a yard, (D) $5.81 which is 3 feet. Therefore, 2 meters is a little more than 6 feet. This is close to the height of a stop sign, so the correct answer is Content Category: Number Sense and Operations with (A). Choice (B) is more than 18 feet, which is too high. There are Fractions and Decimals / Problem Solving 100 centimeters in a meter. Therefore, 800 centimeters is the The price of watermelon is 83 cents per pound. To find the cost same as 8 meters and 1,000 centimeters is the same as 10 of a 7-pound watermelon you need to multiply 7 times 83 cents, meters. These are also too high. which is 581 cents. This is the same as $5.81. The correct answer, therefore, is choice (D).

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MATHEMATICS Sample Question 25: In a cooking class, John is making Optional Constructed-Response Questions (CTP 4 Only) omelets for 26 children. Each omelet needs 3 eggs. How many dozen eggs does John need? Use drawings, words, or numbers to explain your answer. Show all your work. Sample Question 24: Petra is 4 feet 9 inches tall. Her father is 6 feet 3 inches tall. Petra wanted to find out how much Content Category: Math Communication taller her father is than she is. This question is asking you to figure out how many dozen eggs John needs and to explain how you found your answer. The Here is her work. first step is to figure out how many eggs John needs. If he is making 26 omelets and each omelet needs 3 eggs, he needs 78 5 13 eggs, since 26 x 3 = 78. 6 ft 3 in Next you need to find out how many dozen this is. There are 12 - 4 ft 9 in eggs in 1 dozen. To find out how many dozen is equal to 78 eggs, you divide 78 by 12. 1 ft 4 in 6R6 Petra’s work is not correct. Explain what she did wrong and 12 ) 78 give the correct answer. 72 6 Content Category: Math Communication John needs 6 dozen plus 6 more eggs. So he needs 6 1/2 dozen This question asks students to explain the mistake that Petra or 7 full dozen cartons of eggs. made in her work. She wanted to figure out how much taller her father is than she is. Students need to show all of the steps in finding the correct answer in order to receive a score of 2. They must show work for The first step is to figure out what mistake Petra made. Petra finding the 78 eggs. Then they must show how to find how converts 6 feet 3 inches to 5 feet 13 inches. Since there are 12 many dozen eggs this is. They then need to explain what 6R6 inches in a foot, 6 feet is equal to 5 feet 12 inches. Therefore, 6 means – it is 6 dozen plus another 6 eggs, which is 6 1/2 dozen. feet 3 inches equals 5 feet 15 inches. Petra got 5 feet 13 inches. If John can only buy eggs in 1 dozen cartons, he’ll have to buy 7 She added 10 inches for 1 foot instead of 12 inches. cartons. Here is what she should have done: If students find that John needs 78 eggs but they do not find the correct number of dozens needed, they will receive a 5 15 score of 1. If students answer 6 dozen and work indicates they 6 ft did not know how to handle the remainder, they will also get a score of 1. - 4 ft 9 in 1 ft 6 in Petra’s dad is 1 foot 6 inches taller than Petra. Here’s another way to figure this out. From 4 feet 9 inches to 5 feet is a difference of 3 inches. From 5 feet to 6 feet is a difference of 1 foot. From 6 feet to 6 feet 3 inches is a difference of 3 inches. The total difference from 4 feet 9 inches to 6 feet 3 inches is 1 foot 6 inches. If a student has the correct answer with no explanation (or an incomplete explanation), the student will receive a score of 1. The student will also receive a score of 1 if he or she has a correct explanation but does not give the correct answer.

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VERBAL REASONING VOCABULARY

Sample Question 1: Which lettered pair of words goes Sample Question 4: Choose the word that best fist in the together in the same way as the first pair of words? context of the sentence. HOARD : DISPERSE :: Dr. Martin Luther King, Jr., an advocate of nonviolent protest, (A) obtain : acquire never his belief in this form of resistance. (B) oppose : disapprove (A) conquered (C) save : spend (B) acknowledged (D) donate : support (C) abandoned (D) maintained Content Category: Analogical Reasoning The correct answer to this question is (C). The two terms in the Content Category: Precision original pair have an oppositional relationship: to hoard (to Option (C) is the correct answer because the sentence makes accumulate or stockpile) is the opposite of to disperse (to the most logical sense when “abandoned” is inserted in the scatter or disseminate). Only the words in option (C) are also blank. To answer the question, students must recognize that opposites. “this form of resistance” in the sentence is a reference to “nonviolent protest,” of which Dr. King was an advocate. Therefore, options (B) and (D) do not make sense in the context of the sentence; Dr. King would clearly have acknowledged and Sample Question 2: Which of the following words does maintained a belief in something he advocated. The word NOT belong with the others? “conquered” in option (A), while closer in meaning to (A) Planet “abandoned,” does not fit logically or idiomatically. (B) Spaceship (C) Meteor (D) Asteroid Sample Question 5: Choose the pair of words that best fits Content Category: Categorical Reasoning /Fit in the context of the sentence. The correct answer to this categorical reasoning problem is (B). Walking into the museum with a feeling of and All of the objects on the list can be found in outer space; expectation, Magda was so to get started that she however, planets, meteors, and asteroids are all naturally overlooked the map posted at the entrance. occurring, while spaceships are made by humans. (A) boredom . . eager (B) dread . . happy (C) excitement . . anxious Sample Question 3: If most mountains have jagged peaks, (D) anticipation . . unwilling and if Stowe is a mountain in Vermont, then Content Category: Precision (A) Stowe is the only mountain in Vermont with a jagged peak. In this question, the students are looking for precise words that (B) All things with peaks are mountains. make the most logical sense in the sentence. The first blank (C) Stowe is probably over 15,000 feet high. reveals that Magda’s feelings are linked to ones of (D) Stowe probably has a jagged peak. “expectation.” The sentence also indicates that she “overlooked” information. In what circumstances would Content Category: Logical Reasoning /Deductive “expectation” about something cause one to “overlook” crucial Reasoning In this deductive reasoning problem, the information? (C) is the correct answer. One who shows premises are that Stowe is a mountain and that most “excitement and expectation” could become so “anxious” as to mountains have jagged peaks. The conclusion to be drawn, not take notice of things. therefore, is that Stowe probably has a jagged peak. The correct answer, then, is (D).

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READING COMPREHENSION Sample Question 6: What did early archaeologists rely on? (A) Touch (B) Sound Questions 6-10 are based on the following passage. (C) Sight (D) Smell Locating Buried Tombs and Towns Content Category: Explicit Information / Detail This question asks students to recall explicit information from Most of the first places the beginning of the passage. This information is important investigated by the because it helps establish the importance of the use of treasure hunters and technology by modern archaeologists. While early Line early archaeologists were archaeologists had to rely on their sense of sight to discover 5 clearly visible: big artifacts, modern archaeologists have the benefit of technology mounds, ruins of cities, to help them locate buried ruins and objects. The correct and stone monuments. answer, therefore, is (C). Today, there are ways of finding ancient things that may not be visible at all. 10 Photographs of the ground taken from an aircraft directly overhead can reveal the presence of buried Sample Question 7: The passage mentions all of the ruins, ancient roads and ditches, or burial mounds following technological tools EXCEPT that have eroded away to almost nothing. Deep soil is usually thickly covered with vegetation, but soil that (A) infrared photography 15 is shallow because there is something under it, such (B) convection heat as an ancient stone wall, can support only a few (C) ground-penetrating radar plants, and shows up on an aerial photo as a streak (D) magnetometer that looks very different from everything around it. A slight swelling of a worn-down burial mound may Content Category: Explicit Information / Detail 20 not even be noticeable to a person standing right in This question asks students to recall which tools are discussed front of it, but at sunrise and sunset it will cast a in the passage and to recognize which tool is not discussed. longish shadow that reveals its presence perfectly on Convection heat is the one tool that is not mentioned in the a photo taken from above. passage, so the correct answer to this question is (B). The first aerial photographs that produced a major 25 archaeological find were taken over the Sinai Desert in 1920. They showed that several ancient cities were lying beneath the sand! Today, in addition to Sample Question 8: Aerial photographs of the Sinai Desert standard aerial photography, archaeologists make taken in 1920 revealed for the first time the use of special methods. Infrared photography can (A) beautiful shadows in the desert 30 reveal buried objects. Photography from space can (B) plants that grow in the desert reveal details on the Earth’s surface that are not (C) magnetic field around the desert visible at closer distances. It can pick up the course (D) ruins of cities buried in the desert of ancient roads and track them to the sites of buried cities. Content Category: Explicit Information / Detail 35 There are also tools of modern technology that are This question asks students to recall information provided in the helpful in searching for buried tombs and towns beginning of the second paragraph. This information is from the surface of the ground rather than the air. important to the main idea of the passage. The photographs One of these is ground- penetrating radar, which “showed that several ancient cities were lying beneath the sand” sends radio waves into the ground. If the waves (lines 26-27), the first example of technology enabling 40 strike a buried object, they bounce back and form an archaeologists to find ruins not directly visible to the eye. The image on a kind of television screen. Ground- correct answer, then, is (D). penetrating radar is capable of such things as locating ancient communities that are buried under tons of volcanic ash. Another tool is a device known 45 as a magnetometer. The Earth has a magnetic field all around it, and a magnetometer can measure tiny differences in the field that are caused by such things as buried stone walls and buildings. A magnetometer can detect objects buried as deep as 15 feet (4.5 meters) underground.

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Questions 11-14 are based on the following passage. READING COMPREHENSION CONTINUED

Sample Question 9: Which of the following statements is an opinion? (A) Technology has been helpful in searching for burial sites. (B) A magnetometer can detect objects buried as deep as 15 feet. (C) The most valuable finds in the desert are burial mounds. (D) Photography from space can reveal details on the Earth’s surface.

Content Category: Inference / Fact or Opinion This question asks students to distinguish between factual statements and opinions. Options (B) and (D) are statements of fact taken directly from the passage: (B) from lines 48-50 and Maple Syrup Buckets (D) from lines 30-32. Option (A), because it does express a judgment, may look like an opinion, but the content of the At the edge of Mr. Wells’ woods passage clearly presents as fact the notion that technology has I count eighteen rusty buckets been helpful to archaeologists. Only option (C) offers an hanging from maple trees. opinion that cannot be supported by the passage. Therefore, Line In these parts it’s a known fact the correct answer is (C). 5 that Mr. Wells has never smiled in fact hardly speaks at all though he once explained to me why it takes forty gallons of sap Sample Question 10: The passage suggests which of the to make a single gallon of syrup following about technology? 10 which made me wonder if maybe (A) It has proven to be very useful to archaeologists. he requires forty hours of silence (B) It will eventually replace archaeologists. to make a single hour of talk. (C) It can lead archaeologists to wrong conclusions about ancient peoples. He keeps bees, too: succulent honey. (D) It cannot replace human instinct. Strange that such a sour man should 15 produce all that sweetness. Content Category: Analysis / Draw Conclusions This question asks students to infer the role of technology in the field of archaeology today. Although (C) and (D) are both plausible options, since they express reasonable concerns people might have about technology, the passage only Sample Question 11: What does Mr. Wells do? addresses technology’s positive contributions to archaeology. (A) He plants trees. Therefore, (A) is the correct answer. (B) He makes syrup. (C) He repairs buckets. (D) He talks about his bees.

Content Category: Explicit Information / Detail This question asks students to recognize a detail from the poem, namely what Mr. Wells does. According to the poem, Mr. Wells explains to the speaker that “it takes forty gallons of sap to make a single gallon of syrup” (lines 8-9), and the poem ends with the speaker marveling that “such a sour man should produce all that sweetness” (lines 14-15). These details indicate that Mr. Wells makes maple syrup; the correct answer, therefore, is (B).

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READING COMPREHENSION CONTINUED

Sample Question 12: According to the poem, which of the following statements about making syrup is true? (A) It takes forty hours to collect a gallon of sap. (B) Large amounts of sap are needed to produce a gallon of syrup. (C) Bees produce a gallon of honey faster than a person can make a gallon of syrup. (D) Mr. Wells is well known for his unusual methods for making syrup.

Content Category: Explicit Information / Detail In this question, students are to recall basic information contained in the poem. Option (A) might seem correct because of its reference to “forty” and “a gallon of sap”; however, this choice is incorrect because the poem indicates “forty gallons of sap [are needed] to make a single gallon of syrup” (lines 8-9). Option (B) best conveys the notion that a lot of sap is needed to make a small amount of syrup, and therefore (B) is the correct answer.

Sample Question 13: Which of the following statements most accurately describes Mr. Wells? (A) Mr. Wells enjoys visitors. (B) Mr. Wells is talkative. (C) Mr. Wells works slowly. (D) Mr. Wells is unpleasant.

Content Category: Inference / Motives and Behaviors The correct answer is (D). This question requires students to infer what type of person Mr. Wells is. The poem indicates that Mr. Wells “has never smiled [and] in fact hardly speaks at all.” He is also described as being a “sour man.” These descriptions are most indicative of someone who is “unpleasant.”

Sample Question 14: According to the poem, what makes the poet certain that Mr. Wells has never smiled? (A) Mr. Wells told him that he doesn’t smile. (B) Mr. Wells’ family volunteered this information. (C) Other people smile more than Mr. Wells does. (D) No one living nearby has seen Mr. Wells smile.

Content Category: Analysis / Draw Conclusions To answer this question correctly, students need to draw a conclusion about information mentioned in the poem. Nothing about Mr. Wells’ family is mentioned, so option (B) can be eliminated. Option (C) might be true but is also not mentioned or suggested in the poem, and (A) is highly unlikely, since the poem indicates he “hardly speaks at all.” Only option (D) most closely reflects the sentiments expressed in the poem.

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READING COMPREHENSION Sample Question 15: How does lava look when it erupts? Optional Constructed-Response Questions (CTP 4 Only) Discuss two examples from the passage.

Content Category: Reading for Understanding In order to receive a 2 (the highest score) on this question, the student must show clear and solid understanding of how lava Read Passage 1 to learn more about volcanoes. looks when it erupts from a volcano; the response must include A volcano is a vent, or opening, on Earth’s surface where at least two of the following descriptions from the passage. melted rock, called magma, can escape from inside Earth. • a river of fiery water Magma, a slushy mixture of gases, liquid rock, and • bright colors of yellow, orange, and red minerals, is formed in Earth’s interior. Once magma • spilling out of the vent and down the volcano’s slope leaves the vent, it is called lava. With its bright colors of • glowing spray of lava or a lava fountain yellow, orange, and red, flowing lava often resembles a river of fiery water. Sometimes lava erupts quietly, spilling In order to receive a score of 1, the student must show basic out of the vent and down the volcano’s slope. Other times, (but in some way incomplete) understanding of how lava looks pressure from gases forces a glowing spray of lava to shoot when it erupts from a volcano; the response must include one out of the vent, creating a lava fountain. Lava fountains of the descriptions listed above. usually spout anywhere from a few inches to about 30 feet (9 m) into the air. The highest lava fountain ever recorded A score of 0 indicates that the student shows very little or no on Earth came from Hawaii’s Kilauea Volcano in 1959. understanding of how lava looks when it erupts from a volcano; This amazing fountain soared about 1,900 feet (570 m) a response in this category includes none of the descriptions into the air. That’s several hundred feet higher than the listed above or gives only incorrect information. world’s tallest building! Despite our fear of volcanoes’ power, some effects of an eruption are beneficial. Air and rain react chemically with lava, producing very rich soil. This can happen in as little time as one year. In Hawaii, Central America, and South America, pineapples and coffee beans — two economically important crops — thrive in the rich volcanic soil. Also, the heat generated by magma turns groundwater into water vapor. This steam can be used to produce geothermal energy. By drilling into the ground and piping steam or very hot groundwater into power plants, we can produce electricity to light and heat our homes and businesses. New Zealand, Mexico, and the United States are some of the countries that use geothermal power. In Iceland, groundwater is not hot enough to turn into steam, but it is hot enough to pipe directly into homes to heat them. It’s clear that volcanoes not only shape Earth’s surface, but they also affect our lives!

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READING COMPREHENSION CONTINUED Sample Question 16: Both the passage about volcanoes Optional Constructed-Response Questions (CTP 4 Only) and the passage about Mount Vesuvius describe volcanic eruptions. How do these passages differ in their descriptions of the eruptions? Use examples from both passages to support your points. Passage 2 is a fictional account of the eruption of Mount Vesuvius. Content Category: Reading for Understanding In order to receive a 2 (the highest score) on this question, the In the seaside town of Herculaneum, this summer student must show clear and solid understanding of how the morning in the year A.D. 79 seemed like any other. On the two passages differ in their descriptions of volcanic eruptions. beachfront, the fishermen pulled up their boats in front of The response must indicate that the first passage emphasizes the seawall. Breezes from the bay cooled the wealthy the positive aspects of volcanic eruptions (e.g., color, beauty, Romans relaxing in the gardens of their elegant summer dramatic effects, environmental benefits), while the second villas. No one suspected that within hours the top of passage emphasizes the negative aspects of volcanic eruptions nearby Mount Vesuvius would blow off, burying the town (e.g., violence, destruction, frightening appearance). The and many of its people under an enormous avalanche of student must provide specific details from both passages to mud and ash. support claims. Petronia, a servant girl, was busy helping the household In order to receive a score of 1, the student must show basic prepare for a big party. She had spent the past week (but in some way incomplete) understanding of how the two shopping, cooking, and cleaning for the special event. By passages differ; the response might lack specific details or that afternoon, life, as she knew it, was over. Outside, the might refer only to the descriptions from one passage or might sky grew very dark, and the air was thick with hot dust describe differences inaccurately or inadequately. that stuck in her throat and made her eyes water. Screaming, pushing crowds on donkeys, horses, even A score of 0 indicates that the student shows very little or no oxen and cows filled the streets. understanding of how the two passages differ; a response in this category includes no correct descriptions or details from As Petronia looked back at Mount Vesuvius, her heart either passage. almost stopped with fear. The peak of Mount Vesuvius seemed disfigured, as if a giant axe had ripped open the mountain. The mouth of the mountain was outlined in a blaze of red flame, and glowing rocks bubbled out below a gigantic plume of smoke and ash. Petronia turned away from the crowds and escaped to the sea. The ash and hot gas poured over the town, followed by waves of hot mud. In a few hours, Herculaneum was completely buried under 65 feet of volcanic matter, which, when it cooled, covered the town like a cement shield. And so the town lay tightly sealed for about 1,500 years.

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WRITING MECHANICS Sample Question 20: Which of the following should be two sentences? (A) The emperor glanced in all directions while the flying man soared in the morning wind. Sample Question 17: Find the misspelled word, if there is (B) He saw a farmer watching the sky and noted where the one. farmer stood. (C) The emperor reached out a thin hand to touch the birdlike (A) soldier apparatus. (B) separate (D) I rose in the night and walked to the cliffs far away when (C) exagerate the morning breezes blew I gathered my courage. (D) no error Content Category: Usage / Sentence Boundaries Content Category: Spelling / Commonly Used Words This question asks students to identify a run-on sentence that This question asks students to identify an incorrectly spelled should be made into two separate sentences. Options (A) and word. Since the word exaggerate is misspelled, the correct (B) may appeal to students, since (A) is a complex sentence and answer is option (C). (B) has a compound verb. Both (A) and (B) are grammatically correct, however. The only run-on sentence is (D), so (D) is the correct answer.

Sample Question 18: Find the punctuation error in the sentence, if there is one. WRITING CONCEPTS AND SKILLS In cities across the United States, childrens’ museums have (A) (B) attracted young people interested in scientific exploration and (C) Sample Question 21: Decide which is the best order for artistic experiences. No error the sentences listed. (D) 1. The Romans found a way to build the supporting piers of bridges without having to work under water. Content Category: Punctuation / Apostrophe This question asks students to recognize an error in 2. Once the water inside the poles was pumped out, the punctuation. The word childrens’ should have an apostrophe workers would climb down and construct a pier of stone before the “s” instead of after the “s” to express the possessive using the space inside the poles. case of a collective noun. Therefore, option (B) is the correct 3. First, a circle of long wooden poles with pointed ends was answer. driven into the riverbed. 4. Then the poles were chained together and any gaps were filled with clay. Sample Question 19: Choose the word that best (A) 3, 4, 2, 1 completes the sentence. (B) 1, 2, 3, 4 (C) 1, 3, 4, 2 The children were eating lunch in their backyard it (D) 1, 3, 2, 4 began to rain. (A) so Content Category: Organization / Logical Sequence (B) because This question asks students to put four sentences in order to (C) soon form a coherent paragraph. Students must be able to recognize (D) when the topic sentence and then determine the logical sequence of the remaining sentences. Sentence 1 is the only one broad Content Category: Usage / Diction enough to serve as a topic sentence, and while the topic This question asks students to chose the word that correctly sentence need not always come first in a paragraph, in this and grammatically establishes the most likely relationship case it is the only one that could logically begin the paragraph. between the two clauses, “The children were eating lunch in The sequence of the remaining sentences is determined by the their backyard”and “it began to rain.” Options (A) and (B) adverbs that begin each sentence and the logical order of the present relationships that don’t make sense, while option (C) actions described. ( The poles must be driven into the riverbed creates a run-on sentence. Only (D) presents a relationship that and chained together before they can serve as a foundation for both makes sense and creates a grammatically correct a pier.) The correct answer to this question, then, is option (C). expression: The children were eating lunch in the yard when it began to rain.

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WRITING CONCEPTS AND SKILLS options discuss Rachel Carson as a scientist; therefore, students must distinguish between interesting statements CONTINUED about Carson and statements that discuss her research on marine life. Only option (D) discusses Carson’s marine research, so (D) is the correct answer. Sample Question 22: This is a list of major topics in a report on the life of Harriet Tubman. They are not in the correct order. Sample Question 24: The sentence at the beginning of 1. Growing up on a plantation in the South. the question is the main idea of a paragraph. Decide which of 2. Working for the Underground Railroad before the Civil War. the choices goes best with the main idea. 3. Escaping to the North before the Underground Railroad was Some jobs in a city are performed by people for no pay. established. (A) Citizens volunteer to work in schools and help in nursing 4. Serving as a nurse, cook, scout, and spy during the Civil homes and hospitals. War. (B) Unemployment and homelessness are some of the problems people face in a city. Which of these shows the topics arranged in the correct order? (C) People often enjoy cultural performances such as (A) 1, 3, 2, 4 symphonies, ballet, and theater. (B) 2, 1, 4, 3 (C) 3, 1, 2, 4 (D) Trash collection, snow removal, and road maintenance are (D) 4, 3, 2, 1 some of the jobs performed by workers employed by the city. Content Category: Organization / Logical Sequence This question asks students to arrange a list of topics for a Content Category: Supporting Details / Relevant biographical report in the correct order. Since a biographical Information This question asks students to choose the report often follows the subject’s life chronologically, and since sentence that provides the appropriate supporting details for these topics emphasize the time periods during which each the preceding statement. Since the preceding statement refers activity took place, chronological order seems the most logical to jobs in a city that are performed by people for no pay, the choice. Therefore, the student must arrange the topics so that correct answer should give examples of these jobs. (A) is the the list begins with Tubman’s childhood, continues through only option that describes volunteer work; therefore, the the years preceding the Civil War, and concludes with the Civil correct answer is (A). War period. (A) is the only option that begins with Tubman’s childhood and then proceeds chronologically. Thus, (A) is the correct answer. Sample Question 25: Choose the opening sentence that goes best with the details in the paragraph. . Glassmakers in Venice, Italy, Sample Question 23: Which of these would be the best to learned hundreds of years ago to swirl colors through their use in an essay about a famous scientist’s research on marine glass. No two pieces of this glass have exactly the same pattern life? of colors. Today, Venetian glass is still very popular. (A) Rachel Carson was a famous scientist. Her grandmother, a (A) Venice, a city in Italy, is popular for its many canals. teacher, taught her mathematics. (B) Silica and sand are important materials used in (B) I am writing a biography of Rachel Carson. She was a glassmaking. scientist who studied nature. (C) Glass is used to make eyeglasses, telescopes, and (C) Silent Spring is Rachel Carson’s best known book. microscopes. It was one of the first books to expose the dangerous effects of pesticides on the environment. (D) In addition to being useful, Venetian glass is also unique. (D) Rachel Carson began work on The Sea Around Us in 1948. She gathered information for the book while on a ten-day Content Category: Supporting Details / Topic Sentences voyage on a research boat owned by the Fish and Wildlife This question asks students to choose the best topic sentence Service. for a paragraph on Venetian glass. The best topic sentence will introduce the subject matter that is developed in the Content Category: Purpose, Audience, and Focus / Relevant paragraph. Although each of the options discusses glass or Information This question asks students to determine which glass-making, only (D) introduces the idea of the uniqueness of option contains the most appropriate information to include in Venetian glass, a key point in the paragraph. Therefore, option an essay on Rachel Carson’s research on marine life. All of the (D) is the correct answer.

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QUANTITATIVE REASONING The remainder The remainder when 111,111,111 when 111,111,111 is divided by 3 is divided by 9 A B B C Sample Question 27: Which statement is true? (A) A is greater than B. (B) B is greater than A. (C) A and B are equal. 3 (D) There is not enough information to tell which is greater.

Content Category: Extensions and Generalizations The sum of the digits of 111,111,111 is 9. This means that it is divisible by 9 and also by 3. The remainder when 111,111,111 is divided by 3 is 0, and the remainder when 111,111,111 is divided A D by 9 is 0. Therefore, the remainders in A and B are equal, and the correct answer is choice (C). The circumference of the The perimeter of square circle ABCD A B

Plastic Blue Sample Question 26: Which statement is true? Blocks Blocks (A) A is greater than B. (B) B is greater than A. (C) A and B are equal. (D) There is not enough information to tell which is greater. The number of The number of plastic blocks blue blocks Content Category: Comparison A B The square “sticks out” more than the circle. If you needed to travel from point A around the square and back to A again, you Sample Question 28: Which statement is true? could shorten your trip by traveling part of it on the circle. (A) A is greater than B. Therefore, the perimeter of the square is greater than the (B) B is greater than A. circumference of the circle. This question can also be (C) A and B are equal. approached by using the fact that the radius of the circle is 3 (D) There is not enough information to tell which is greater. and the length of each side of the square is 6. The circumference of the circle is 2πr = 6π (which is between 18 and Content Category: Analysis 19). The perimeter of the square is 4 x 6 = 24. Since 24 > 6π, the The Venn diagram allows for the possibility that some blocks perimeter is greater than the circumference. Therefore, the are plastic and not blue, some are plastic and also are blue, amount in B is greater than the amount in A. The correct some are not plastic but are blue, and some are neither plastic answer is (B). nor blue. No numbers are given for any of these categories, so there is no way to compare the number of plastic blocks with the number of blue blocks. Therefore, there is not enough information to tell which amount is greater. The correct answer is choice (D).

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QUANTITATIVE REASONING CONTINUED MATHEMATICS

Sample Question 30: Which of the following is less than 7/8? (A) 9/10 (B) 8/9 (C) 3/4 (D) 15/16

Content Category: Numbers and Number Relationships / Conceptual Understanding The fraction7/8 is 1/8 less than 1. Sample Question 29: Scott is using a mirror with the The fraction9/10 is 1/10 less than 1. Since 1/10 is less than 1/8, it drawing above to form images. Which of the following images follows that 9/10 is closer to 1 than 7/8 is. Therefore,7/8 < 9/10. can he form? Similar thinking will show that 7/8 < 8/9 and 7/8 < 15/16. Alternatively, to compare 7/8 with 3/4, rewrite 3/4 as 6/8. It is clear that 6/8 < 7/8. Therefore, 3/4 < 7/8. The correct answer is choice (C).

Sample Question 31: Five consecutive whole numbers sum to 125. What are the numbers?

(A) 18, 19, 20, 21, and 22 (B) 21, 22, 23, 24, and 25 (C) 23, 24, 25, 26, and 27 (A) (B) (D) 25, 26, 27, 28, and 29

Content Category: Number Systems and Number Theory / Problem Solving The middle number of the five consecutive whole numbers is also the average of the five consecutive whole numbers. That middle number is 125 ÷ 5, which is 25. To make 25 the middle number, you would start with 23. The five numbers are 23, 24, 25, 26, and 27. An alternate approach is to add up the five numbers in any option and see if the sum is 125. The only option containing 5 numbers with a sum of 125 is option (C). The correct answer is choice (C). (C) (D)

Content Category: Analysis Sample Question 32: Which of the following could not be Among the answer choices, (A) and (D) can be ruled out a rectangle? because they lack symmetry. Choice (A) lacks symmetry (A) A parallelogram because the eyes in the lower part of the image are not a (B) A polygon reflection of the eyes in the upper part. Choice (D) lacks (C) A trapezoid symmetry because the two necks are unequal in length. (D) A quadrilateral Choice (C) has a vertical line of symmetry, but it is incorrect because a notch appears instead of part of a neck. Choice (B) Content Category: Geometry / Conceptual Understanding can be formed by placing an edge of the mirror on a vertical A parallelogram could be a rectangle (if it happened to have line just to the left of the center of the original drawing. The right angles). A polygon could be a rectangle (if it happened to right-hand side of the image is in the original drawing, and the have four sides and four right angles). A quadrilateral could be left-hand side of the image is the reflection in the mirror. The a rectangle (if it happened to have four right angles). The correct answer, therefore, is choice (B). reason a trapezoid can never be a rectangle is that a trapezoid must have one pair of opposite parallel sides and one pair of opposite nonparallel sides. In a rectangle, both pairs of opposite sides are parallel. The correct answer is choice (C).

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MATHEMATICS CONTINUED

Sample Question 33: The four points with coordinates (1, 2), (1, 5), (3, 5), and (4, 2) are to be connected to make a Z as Sample Question 35: What is the area of the figure shown. In what order can they be connected? above? (A) (1, 2) (1, 5) (3, 5) (4, 2) (A) 74 square centimeters (B) (1, 5) (3, 5) (1, 2) (4, 2) (B) 68 square centimeters (C) (3, 5) (1, 5) (1, 2) (4, 2) C) 65 square centimeters (D) (4, 2) (3, 5) (1, 5) (1, 2) (D) 49 square centimeters

Content Category: Geometry and Spatial Sense / Conceptual Content Category: Measurement / Problem Solving Understanding To connect the four points, you would begin The figure consists of two rectangles and a triangle. One either at (1, 5), the point at the upper left of the Z, or at (4, 2), the rectangle has dimensions 4 cm by 8 cm. Therefore, its area is 32 point at the lower right of the Z. If you begin at (1, 5), the next square centimeters. The other rectangle has dimensions 3 cm point should be the one to the right of (1, 5), namely (3, 5). The by 8 cm. The length of 8 cm is found by comparison with the point after that should be the one on the lower left, (1,2), and length of the first rectangle. The second rectangle extends 2 cm the last point should be to the right of (1,2), namely (4, further on the upper end, but starts 2 cm higher on the lower 2). This is the sequence shown in answer choice (B), which is end, 8 + 2 – 2 = 8. Therefore, the area of the second rectangle is the correct answer. Answer choice (D) begins with (4, 2). If 24 square centimeters. you started at (4, 2), the next point should have been (1, 2). In option (D) the first point listed is (4, 2), and the second is The triangle has base 3 cm and height 6 cm (8 – 2 = 6). The area (3, 5). So option (D) is not correct. of the triangle is ½ × 3 × 6 , which is 9 square centimeters Therefore, the total area is 32 + 24 + 9, or 65 square centimeters. The correct answer is choice (C).

Length = 4x

Width = x

Sample Question 34: The length of a rectangular garden is four times its width. The perimeter of the garden is 240 meters. What is the length of the garden? (A) 24 meters (B) 48 meters (C) 96 meters (D) 192 meters

Content Category: Measurement / Problem Solving Using the information about the rectangle’s dimensions and perimeter, you can write the equation 4x + x + 4x + x = 240. Since 10x = 240, it follows that x = 24. The question asks for the length of the garden, 4x, which is 4 x 24 or 96. The correct answer is choice (C).

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MATHEMATICS CONTINUED Sample Question 37: How many of the Grammy award winners shown in the table have won more Grammys than the median number of Grammys won by all 10 winners? (A) Three (B) Four (C) Five (D) Six

Content Category: Statistics / Problem Solving The table lists the Grammy award winners in order from the one with the greatest number of awards to the one with the least number of awards. The median number of Grammys won by all 10 winners is the average of the two middle numbers, 15 and 16; thus, the median is 15 ½. There are five winners listed who have won more than 15 ½ awards. The correct answer is Sample Question 36: Ray MR above moves around point choice (C). M in a clockwise direction until it is on top of ray MK. How many degrees does ray MR move? (A) 90° Sample Question 38: According to the table, what is the (B) 180° range in the number of Grammys awarded? (C) 270° (A) 7 (D) 360° (B) 9 (C) 11 Content Category: Measurement / Conceptual (D) 13 Understanding Ray MR will move through three quarter circles. The first quarter circle will result in the ray opposite ray Content Category: Statistics / Problem Solving MK. The second quarter circle will result in the ray opposite the The range refers to the difference between the highest value initial position of ray MR. The third quarter circle will result in and the lowest value. For the data in the table, the highest a ray on top of ray MK. Each quarter circle measures 90°, and 3 number of Grammys awarded is 26 and the lowest number of x 90 = 270°. The correct answer is choice (C). Grammys awarded is 13. Therefore, the range is 26 — 13, which is 13. The correct answer is choice (D).

Questions 37 and 38 refer to the table below. Sample Question 39: A number cube has a different TOP TEN GRAMMY AWARD WINNERS, 1999 number from 1 to 6 on each face. If the number cube will be Winner Number of Grammy Awards rolled twice, what is the probability that the sum of the numbers on the top face of the cube will be 10? Qunicy Jones 26 Henry Mancini 20 (A) 1/12 (B) 1/10 Stevie Wonder 19 (C) 1/6 Paul Simon 16 (D) 2/3 John Williams 16 Aretha Franklin 15 Content Category: Probability / Problem Solving Chet Atkins 14 There are 36 combinations that result from rolling the cube twice. You need to count the number of combinations for David Foster 14 which the sum of the numbers on the top face is 10. Ella Fitzgerald 13 Michael Jackson 13 1st roll 2nd roll 4 6 5 5 6 4

There are 3 combinations giving a sum of 10. Therefore, the probability that the sum will be 10 is 3 out of 36, or 1/12. The correct answer is choice (A). 74 | CTP CONTENT STANDARDS MANUAL CTP OPERATIONS OFFICE · (866) 683-2335 or (646) 503-2699 · [email protected] SAMPLE QUESTIONS: LEVELS 4-6

MATHEMATICS Optional Constructed-Response Questions (CTP 4 Only)

Sample Question 40: Here are some clues about a certain whole number. • It is a multiple of 3. • Its square is an even number less than 100. What is the number? Explain your reasoning.

Content Category: Math Communication It is given that the number is a multiple of 3, and its square is an even number less than 100. The even squares less that 100 are 4, 16, 36, and 64. The square roots of these squares are 2, 4, 6, and 8. Of these square roots, only 6 is a multiple of 3, so 6 is the only positive integer that satisfies both conditions. Alternative solutions are possible. Students receive full credit (a score of 2) if they answer 6 and have a mathematically correct explanation. Students receive partial credit (a score of 1) by: 1) Answering 6 with an incomplete explanation or no explanation. Or 2) Answering 36 with an explanation that includes 6 = 36 and 36 < 100.

Sample Question 41: Each day Mrs. Kistler drives 48 miles to work and 48 miles back home again. • Her car uses 1 gallon of gas for every 30 miles she travels. • Last week she worked 5 days. How many gallons of gas did she use last week going to work and back? Show your work or explain how got your answer.

Content Category: Math Communication Mrs. Kistler drives 96 miles each day. In the 5 days she worked last week her total mileage is 5 x 96 or 480 miles. Her car uses 1 gallon of gas for every 30 miles. 480 ÷ 30 = 16. The correct answer is 16 gallons. Alternative approaches are possible. For example, Mrs. Kistler drives 96 miles each day. Since 96 ÷ 30 = 3.2, she uses 3.2 gallons of gas each day. Over the course of 5 days she uses 32 x 5 or 16 gallons of gas. Students receive full credit (a score of 2) if they answer 16 gallons and show mathematically correct work or explanation. Students receive partial credit (a score of 1) if they: 1) give the correct answer with no work or incomplete/unclear work, 2) have the correct process, but do not get the correct answer, or 3) answer 8 gallons and show work for only the one-way journey instead of the round-trip journey.

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VERBAL REASONING VOCABULARY

Sample Question 1: Which lettered pair of words goes Sample Question 4: Choose the word that best fits in the together in the same way as the first pair of words? context of the sentences. MELODIOUS : SOUND :: The talk show host’s popularity was based on her ability to (A) peaceful : noise generate dialogue with her guests. The witty (B) evident : view conversation ensured high ratings with a large audience. (C) tasty : flavor (A) onerous (D) malodorous : smell (B) listless (C) scintillating Content Category: Analogical Reasoning (D) mundane The correct answer to this reasoning problem is (C). There is a positive, associational relationship between the two terms in Content Category: Precision the pair: a sound that is melodious is by definition pleasing. This question asks students to choose the word that best fits in Only the pair of words in option (C) has this same relationship. the context of these sentences. Since the sentences discuss the host’s popularity and witty conversation with her guests, the missing word should emphasize the lively quality of the dialogue. The word “scintillating,” meaning animated and vivacious, is the only one of the choices that emphasizes this Vital quality, so option (C) is the correct answer. Central

Fundamental Sample Question 5: Choose the pair of words that best fits in the context of the sentence. Sample Question 2: Which of the following words best fits Although Ron disagreed with his friend, instead of in the list above? him directly, Ron tried to express his own idea more (A) Bothersome . (B) Basic (A) supporting . . secretly (C) Stray (B) contradicting . . diplomatically (D) Initial (C) attacking . . meekly (D) affirming . . reliably Content Category: Categorical Reasoning / Fit The correct answer to this question is (B). Each of the three words in the list defines something that is “essential or of Content Category: Precision primary concern.” Only option (B) conveys this same meaning. The pair of words that makes the most sense in this sentence is the pair in option (B): contradicting . . diplomatically. Options (A) and (D) can be eliminated based on the first word in each pair; the first blank can be filled logically only by something Sample Question 3: Complete the statement below by that reinforces the idea that Ron is in disagreement with his selecting the most logical conclusion. friend. Option (C) is plausible at first glance, but “attacking” is too strong — disagreement does not necessarily imply If all mammals are warm-blooded creatures and if all bears are antagonism — and the opposition between “attacking” and mammals, then expressing an idea “meekly” is not as precise as the more (A) bears hibernate because they are warm- blooded creatures logical opposition between “contradicting” and expressing an (B) every warm-blooded mammal is a bear idea “diplomatically.” (C) grizzly bears are warm-blooded creatures (D) full-grown grizzly bears are the largest warm- blooded creatures

Content Category: Logical Reasoning / Deductive The correct answer to this question is (C). The suppositional statement establishes two points: 1) all mammals are warm- blooded creatures; and 2) all bears are mammals. Given this information, only option (C) can be deduced from the information provided.

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VOCABULARY CONTINUED Sample Question 8: Which of the following phrases most nearly means the same as the word scores as it is used in line 2? (A) musical compositions (B) large numbers Sample Question 6: The sales representative had traveled (C) privacy and shelter the same circuit throughout the southeastern United States for (D) indefinitely repeating patterns twenty years before retiring. Which of the following definitions of the word “circuit” is used Content Category: Application / Synonym in the sentence above? The correct answer to this question is (B). In the phrase “scores of places to spend an afternoon,” only “large numbers” makes (A) Periphery sense in place of “scores,” which is defined in this context as “a (B) Route great many.” (C) Assemblage (D) League

Content Category: Application Sample Question 9: Which of the following words is more This question asks students to choose the correct definition of precise than the word never-ending in line 9? the word “circuit” in the context of a sentence. One meaning of “circuit” is the line going around or bounding any area or (A) incessant object, making option (A) attractive, but “periphery” does not (B) raucous make sense within the context of the sentence. The only option (C) interrupted that makes sense in this context is (B), “route,” which matches (D) occasional the definition of a circuit as the route followed on a periodical journey made to perform certain duties. Therefore, option (B) is Content Category: Application / Synonym the correct answer. In this question, the students are looking for a word that is more precise in meaning than “never-ending.” Option (A) is the correct answer because that which is “incessant” is by definition continual and “never-ending.” Sample Questions 7-10 are based on the passage below.

Deep and shaded by alders, this perennial creek Sample Question 10: Which of the following phrases has carved a canyon that offers scores of places to most nearly means the same as the word babble in line 9? spend an afternoon. The canyon’s beauty begins at road’s edge. Alders thickly covered with green (A) jovial conversations leaves flutter in the breeze, and twenty yards (B) private conversations upstream are the first pools. With the canyon (C) friendly movements walls and alder boughs for privacy, sandstone (D) sounds with no specific meaning boulders for resting spots, and the creek’s Line 9 never-ending babble for companionship, you’ll Content Category: Application / Synonym fall in love with it in 5 no time. This question asks the students to recognize that “babble” means “meaningless or unintelligible sounds”; therefore, the correct answer is (D).

Sample Question 7: Which of the following phrases most nearly means the same as the word perennial in line 1? (A) specific to one place (B) winding around (C) constant throughout the seasons (D) pretty and delightful

Content Category: Application / Synonym The wordperennial in this context means lasting or enduring for an indefinitely long time, especially in terms of remaining unchanged throughout the seasons of the year. Therefore, option (C) is the best answer.

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READING COMPREHENSION Sample Question 12: The phrase “they don’t quit” (line 17) suggests all of the following about the ants EXCEPT: (A) They seem almost infinite in number. (B) They are extremely flexible. Questions 11-16 are based on the following passage. (C) They do not stop moving. (D) They travel great distances.

The World of the Amazon Jungle Content Category: Inference / Draw Conclusions When you are inside the jungle of the Amazon, away This question requires students to understand the phrase “they from the river, the trees vault out of sight. It is hard to don’t quit” (line 17) in the context of the passage and to remember to look up the long trunks and see the recognize what is not discussed, either explicitly or implicitly, fans, strips, fronds, and sprays of glossy leaves. about the ants. Options (A), (C), and (D) are all mentioned or 5 Inside the jungle you are more likely to notice the implied. Nothing in the passage, however, suggests that the snarl of climbers and creepers around the trees’ ants are “flexible”; therefore, the correct answer is (B). trunks, the flowering bromeliads and epiphytes in every bough’s crook, and the fantastic silk-cotton tree trunks 30 or 40 feet across, trunks buttressed in 10 flanges of wood whose curves can make three high Sample Question 13: The description of the trees mainly walls of a room — a shady, loamy-aired room where emphasizes that they are you would gladly live. Butterflies, iridescent blue, (A) endangered striped, or clear-winged, thread the jungle paths at (B) useful to humans eye level. And at your feet is a path of ants bearing (C) very large 15 triangular bits of green leaf. The ants with their (D) covered with animal life leaves look like a wide fleet of sailing boats — but they don’t quit. In either direction they wobble over Content Category: Analysis / Purpose and Intent the jungle floor as far as the eye can see. This question requires students to use their skills of analysis. Unseen in the jungle, but present, are tapirs, jaguars, Based on the description of the trees in the passage, students 20 many species of snake and lizard, ocelots, are to determine which aspect of the trees the author armadillos, marmosets, howler monkeys, toucans emphasizes. Options (A) and (B) are the easiest to eliminate, and macaws, and a hundred other birds, deer, and for although the trees may well be both endangered and useful bats. Also present in this jungle, but variously to humans, these aspects are not mentioned in the passage. distant, are oil derricks and pipelines, and some of Option (D) is appealing, but the only life mentioned in the 25 the fiercest fighters in the world. passage that is directly supported by the trees is plant life: the “climbers and creepers” around the trees’ trunks and the “bromeliads and epiphytes” in their boughs (lines 6-8). The emphasis in the passage is clearly on the size of the trees. The trees are described as “vault[ing] out of sight” (line 2), with “long trunks” (line 3) that are “30 or 40 feet across” (line 9). Sample Question 11: The main idea of the passage is that Option (C) is therefore the correct answer. (A) the jungle teems with more life than meets the eye (B) danger lurks in unseen places (C) the beauty of the jungle is best appreciated from the river (D) one must remember to look up when inside the jungle Sample Question 14: The descriptions in the passage rely primarily on the sense of Content Category: Explicit Information / Main Idea (A) smell This question asks the students to recognize the main idea of (B) sound the passage. The passage’s detailed description of the various (C) sight plants, animals, and activities in the Amazon jungle clearly (D) touch supports (A) as the correct answer. Content Category: Analysis / Purpose and Intent This question asks students to recognize which sense the author appeals to most in describing the Amazon jungle. The detailed descriptions of the trees’ height and size, the various flowering plants, and the colorful insects appeal most to the reader’s sense of sight. Option (C), therefore, is the correct answer.

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Sample Questions 17-21 are based on the following passage. READING COMPREHENSION CONTINUED

Although we all use postage stamps, few of us think about their origin. Read this account to learn about Sample Question 15: The second paragraph of the their early development. passage primarily serves to Before the postage stamp, there was the postmark. In (A) describe the dominance of machinery over nature England, it took the form of a triangular impression (B) reemphasize the need for conservation in red ink bearing the words “Penny post paid.” From (C) provide a contrast between plant and insect life and 1834 to 1838 an Englishman by the name of human life 5 Chalmers, a printer and bookseller in Dundee, (D) introduce the presence of larger creatures and human printed a kind of postage label that he had invented. beings But the real father of the postage stamp was Roland Hill. In 1837 he published a pamphlet entitled Post Content Category: Analysis / Purpose and Intent Office Reform in which he proposed that letters be In this question, the students are to examine the second 10 carried any distance within Great Britain and paragraph only and determine its purpose. Why has the author Ireland for a fixed rate and that all postage be included this information? In this paragraph, the author prepaid. (At the time, most letters went through the mentions other species of animals that are much larger than mail unpaid, with postage collected on delivery.) the butterflies and ants mentioned earlier. Also, the paragraph Wrappers and envelopes with the postmark includes references to the “oil derricks and pipelines, and some 15 indicating prepayment were to be sold at all post of the fiercest fighters in the world” (lines 24-25), which are offices; and for people who wanted to use their own clearly allusions to the presence of humans. Therefore, (D) is stationery, Hill proposed a bit of paper just large the correct answer. enough to bear the post office’s imprint and “covered at the back with a glutinous wash, which might, by 20 applying a little moisture, attach to the back of the letter.” Sample Question 16: The author’s attitude toward being Hill’s proposal was submitted to the Houses of in the jungle is primarily one of Parliament, where at first it met great resistance. (A) mild discomfort Thanks to publicity generated by the press, however, (B) scholarly interest Hill was able to work out the details of his proposal to (C) anxiety 25 everyone’s satisfaction. On August 17, 1839, a law was (D) awe passed authorizing the use of the adhesive postage stamp, and a competition was held. The subject Content Category: Analysis / Style and Tone chosen for the stamp was Queen Victoria. Henry From information stated in the passage, the students are to Courbould made a drawing from a portrait that had determine the author’s overall attitude toward the jungle. 30 been used by the royal mint for the medal that had Nothing in the passage suggests that the author is been struck commemorating the queen’s first visit to uncomfortable or anxious about being in the jungle; therefore, London in 1837. Above the head of the queen was the (A) and (C) can be easily eliminated. (B) might hold some word “Postage,” and below, a panel with “One Penny” appeal, but the author does not discuss the jungle in a or “Two Penny.” On May 6, 1840, both stamps were scholarly manner. Instead, the author conveys the wonder of 35 ready: the one-penny was black, the two-penny blue. being in the presence of jungle with its teeming life; therefore, The following year, these stamps were sold in every (D) is the correct answer. post office in Great Britain. The postage stamp was enthusiastically adopted by the British public: in 1839, 50 million letters were sent within the country; 40 in 1840, 170 million; and ten years later, more than double that number! The celebrated one-penny black and its companion, the two-penny blue, are now among the rarest stamps in the world and the prize of any collection.

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READING COMPREHENSION CONTINUED Sample Question 20: The passage implies that which of the following happened in 1840? (A) Parliament was still debating Hill’s proposal. (B) The queen’s portrait for the first stamp was painted. Sample Question 17: According to the passage, the (C) Stamps were phased into circulation. triangle of red ink was known as the (D) Collectors rushed to buy the rare stamps.

(A) postage stamp Content Category: Inference / Draw Conclusions (B) postmark This question asks students to infer what happened in 1840. (C) postal label The student needs to recognize a logical sequence of events in (D) postal wrapper order to answer this question correctly. Options (A) and (B) refer to events that took place before 1840. Option (D) refers to Content Category: Explicit Information / Detail an event that would not yet have happened in 1840. Only This question asks students to recall explicit information from option (C) describes an event that would logically have taken the first sentence of the passage. The first sentence indicates place in 1840: if the stamps were ready on May 6, 1840, then it is that the postage stamp was preceded by the postmark, which likely that they were phased into circulation shortly thereafter. was “a triangular impression in red ink” (lines 2-3). Therefore, Moreover, the passage states that by “the following year [1841], the correct answer is option (B). these stamps were sold in every post office in Great Britain.” The stamps must therefore have been phased into circulation in 1840. Option (C) is the correct answer.

Sample Question 18: The term “glutinous wash” (line 19) refers to the (A) ink used to print the stamps Sample Question 21: The passage mentions the numbers (B) paper the stamps were made of of letters sent within Great Britain in order to indicate that (C) coating on the back of the stamps (A) people enthusiastically accepted the postage stamps (D) liquid used in paper manufacture (B) stamps were cheaper than postmarks (C) people corresponded more than they do today Content Category: Inference / Implicit Information (D) mail delivery was much faster after stamps were This question asks students to infer what the term “glutinous introduced wash” refers to in this passage. The passage describes a small bit of paper covered with a glutinous wash on the back (lines Content Category: Analysis / Purpose and Intent 17-19). The paper is then attached to a letter after a little This question asks students to infer the reason for the moisture is added to the glutinous wash. The student must references in the passage to the numbers of letters sent within infer that the bit of paper is a stamp and that the “wash” is the Great Britain after stamps were introduced. In answering this glue that coats the back of a stamp. The correct answer to this question, the student should take note of where these question, then, is (C). references occur in the passage. Options (B), (C), and (D) are plausible reasons for an increase in the number of letters sent, but the information needed to support these statements is not in the passage. Option (A) makes the most sense in the context Sample Question 19: The passage suggests that which of of the passage, especially since the references to the numbers the following helped Hill’s proposal gain acceptance in of letters immediately follow the statement “the postage stamp Parliament? was enthusiastically adopted by the British public.” Clearly, the passage cites the numbers of letters sent in order to show the (A) The press British public’s enthusiasm for the stamp. Option (A), then, is (B) The enthusiasm of the queen the correct answer. (C) Henry Courbould (D) Intense pressure from the post office

Content Category: Inference / Implicit Information This question asks students to determine which factor helped Hill’s proposal gain acceptance in Parliament. The passage states that “Thanks to publicity generated by the press . . . Hill was able to work out the details of his proposal to everyone’s satisfaction” (lines 23-25). Nothing else is cited as a factor in helping Hill’s proposal gain Parliament’s approval. Option (A), therefore, is the correct answer.

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READING COMPREHENSION Sample Question 22: In Passage 1, what elements seem Optional Constructed-Response Questions (CTP 4 Only) to indicate that Galahad was destined to sit in the Perilous Seat, the seat of honor? Discuss at least two of these elements.

Content Category: Reading for Understanding To receive a 2 (the highest score) on this question, the student Passage 1 is a story drawn from legends of King Arthur must show clear and solid understanding of two or more and his knights. elements that indicate that Galahad was destined to sit in the seat of honor; the student must name two or more of the When the knights of the Round Table met at Camelot, following. there rode into the hall a fair lady who went straight to • fair King Arthur and greeted him, saying,“Where is Sir • noble Lancelot?” And the king showed her. Then went she to • well-made him and said,“Sir, come with me into the forest.” Lancelot • no better man beheld by Lancelot and the lady rode forth, and she led him to a youth so fair • no match in the world and well-made that in all the world none could find his • knighted by Lancelot match. His name was Galahad, and Lancelot thought that • lady wanted him knighted he had never beheld a better man. • name written on the Perilous Seat “Sir,” said the lady,“make this youth a knight, for from no • place of honor worthier hand than Lancelot’s can he receive that honor.” • light comes from seat Galahad expressed the same desire. So Lancelot knighted • doors and windows close him. • can draw sword from stone Then Lancelot returned to Camelot. When the knights To receive a score of 1, the student must show basic (but in next gathered in the banquet hall, each found his name some way incomplete) understanding of elements; the student written at a seat in letters of gold. And in “the Perilous must name one the elements listed above. Seat,” the place of honor at the table, a name was also A score of 0 indicates that the student shows very little or no written, and they marveled greatly, for there had never understanding of the elements that indicate that Galahad was been a name there and no knight had ever yet dared to sit destined to sit in the seat of honor; the student is unable to upon that seat. Lancelot covered the name with a silken name any of the elements listed above or lists elements but veil. they are incorrect. When the high feast began, the hall was filled with laughter and talk. But suddenly the doors and windows shut violently all by themselves, making thick darkness, and a fair, gentle light came from the Perilous Seat. Then Arthur rose and said,“Fair knights, rejoice, for I know we shall today see him who may sit in the Perilous Seat.” Then an old man entered, leading young Galahad. The old man took him to the Perilous Seat, and lifting up the silken cloth that had covered the name, read these words:“This is the seat of Sir Galahad, the good knight.” Galahad was taken to a mighty stone that floated in the river and was pierced by a sword inscribed thus:“No man shall take me but the best knight in the world.” “Here,” said the king,“is as great a marvel as ever I saw, and many good knights have tried and failed to gain that sword.” “I do not wonder,” said Galahad,“for this adventure is mine, since I brought no sword with me.” And he laid his hand upon the sword and lightly drew it from the floating stone.

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READING COMPREHENSION CONTINUED Sample Question 23: What does the last paragraph of Optional Constructed-Response Questions (CTP 4 Only) Passage 2 make you think about the relationship between Passage 1 and Passage 2?

Content Category: Reading for Understanding To receive a 2 (the highest score) on this question, the student Passage 2 considers the legend of King Arthur from a must show clear and solid understanding that, although there historian’s point of view. is no definitive proof that Arthur ever existed, the story and the people are realistic, or the story is valuable, or the story is In England archaeologists wonder: did the legendary enjoyable. The student must counterpose the lack of definitive King Arthur really exist, or were he and his knights just a proof to the value or interest or realism of the story; he or she storybook tale? A twelfth-century English monk, Geoffrey may say, for instance, “Although there is no proof or there may of Monmouth, wrote a History of the Kings of Britain that never be proof, the story or the people in the story are realistic claims that the Arthurian stories came from old books (or there is value in the story, or enjoyment in the story, or the and legends, but the tales he recorded were true and set story is exciting or fun).” in Arthur’s time. Many people, however, scoffed, saying that Geoffrey made up the entire legend. To receive a score of 1, the student must show basic (but in some way incomplete) understanding of the relationship The tales about Arthur, featuring castles, dragons, between Passages 1 and 2; the student may give either half of sorcerers, and knights in armor, have constituted the the response described above, but not both halves. principal myth of Britain for nearly a thousand years. Some archaeologists think that the stories are based on A score of 0 indicates that the student shows very little or no the real deeds of a great warrior (not King Arthur) who understanding of the relationship between Passages 1 and 2; a lived at the end of the fifth century A.D. when the Roman response in this category gives none of the response described Empire had collapsed and Anglo-Saxons from Europe above or give an incorrect response. invaded England. All the kings in Britain joined forces to defeat the invaders, and the battles became the subject of stories passed down through time. Arthur’s legends became linked with those of the unknown leader of these battles, and Arthur’s fame grew. Geoffrey of Monmouth tells that Arthur was born at Tintagel in Cornwall, England, and archaeological digs at Tintagel have unearthed luxurious objects, suggesting that the site was someone’s royal stronghold. But whose? The stories also tell how Arthur was wounded in his last battle and taken to the enchanted Isle of Avalon, where he died and was buried. No one really knows Avalon’s location, but in the twelfth century, monks at Glastonbury in England announced that they had unearthed a burial place with the Latin words:“Here lies the renowned King Arthur in the Isle of Avalon.” Beneath the inscription was an oak coffin containing bones and a skull. The medieval description suggests that the tomb could have been a royal grave. Was the tomb Arthur’s? Archaeologists may never find complete evidence that Arthur really existed. But as long as people can read the wonderful Arthurian legends, he and his brave knights seem very real.

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WRITING MECHANICS WRITING CONCEPTS AND SKILLS

Sample Question 24: Find the error in the sentence, if Sample Question 27: This is a list of the major topics in there is one. an article about how to redecorate a room.

“All atheletes need to turn in their uniforms by 1. Buy paint and other materials. (A) (B) 2. Decide on a color scheme. Friday,” announced the coach. No error 3. List what you will need to buy. (C) (D) 4. Comparison shop for the lowest prices.

Content Category: Spelling / Commonly Used Words Which of the following shows the parts of this outline arranged The correct answer to this question is (A). Students are to in the correct order? recognize that “athletes” is misspelled. (A) 2, 1, 3, 4 (B) 2, 3, 4, 1 (C) 3, 4, 2, 1 (D) 4, 3, 1, 2 Sample Question 25: Find the error in the sentence, if there is one. Content Category: Organization / Logical Sequence Even though Simon was tired ; he found the energy This question asks students to arrange a list of topics for an (A) (B) article about redecorating a room. The topics should be to take a long bike ride after school. No error. arranged in a logical sequence of actions, beginning with (C) (D) planning the redecoration and ending with purchasing the necessary materials. Although both options (A) and (B) begin Content Category: Punctuation / Comma versus Semicolon with the initial planning, only (B) proceeds logically from that The correct answer to this question is (B). Students must point. Therefore, (B) is the correct answer. identify the punctuation error in the sentence by recognizing that the semicolon should be replaced with a comma, since “Even though Simon was tired” is a subordinate clause, not an independent one. Sample Question 28: Decide which is the best order for the sentences listed. 1. The pilot and a picked crew go out in a smaller “sounding- Sample Question 26: Find the error in the sentence, if boat” and hunt for the best water. there is one. 2. The pilot sounds the depth of the river with a pole that is ten or twelve feet long. The lyrics of one of the most-known spirituals, “Swing Low, 3. The moment the shallowest point is reached, the pilot (A) delivers the order, “Let go the buoy!” and over it goes. Sweet Chariot,” are repeated several times in order to produce a (B) (C) 4. This is the way that a river “sounding” is done. melancholy theme. No error (A) 1, 3, 2, 4 (D) (B) 2, 3, 4, 1 (C) 3, 2, 1, 4 Content Category: Usage / Diction (D) 4, 1, 2, 3 The correct answer to this question is (A). This usage question tests appropriate diction. Students are to recognize that the Content Category: Organization / Logical Sequence correct word choice for (A) should be either “best-known” or This question asks students to put four sentences in order to “most widely known.” form a coherent paragraph. Students must be able to recognize the topic sentence and then determine the logical order of the remaining sentences. The fourth sentence is the only sentence broad enough to serve as a topic sentence, and while the topic sentence need not always come first in a paragraph, in this case it is the only one that could logically begin the paragraph. The order of the remaining sentences is determined by the logical sequence of the actions described. ( The pilot and crew must first go out in a boat, then use a pole to sound the depths, and finally, drop the buoy when the shallowest point is found.) The correct answer to this question, then, is option (D).

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WRITING CONCEPTS AND SKILLS Sample Question 31: The sentence at the beginning of the CONTINUED question is the main idea of a paragraph. Decide which of the choices goes best with the main idea. Past Presidents have led the country through wars, economics depressions, and periods of geographic expansion. Sample Question 29: Which of the following sentences (A) To be successful, Presidents need various leadership skills would be most appropriate to include in a report on proper and the ability to deal with enormous national challenges. nutrition? (B) Wars are devastating to a nation. (A) Fruits and vegetables grow better in warmer areas of the (C) In order to be President, one must be a United States country. citizen. (B) Fruits and vegetables provide important vitamins and (D) Some Presidents were senators, representatives, or minerals needed for optimal body function. governors before taking office. (C) The federal government regulates meat, poultry, and dairy products. Content Category: Supporting Details / Relevant (D) Fast-food restaurants sell more meat products than fruits Information This question asks students to choose the and vegetables. sentence that is supported by the details in the preceding statement. Since the preceding statement refers to some of the Content Category: Purpose, Audience, and Focus / Relevant weighty responsibilities of past Presidents, the correct answer Information This question asks students to determine which will most likely discuss the general skills that Presidents need sentence provides the appropriate information for a report on to have. Options (C) and (D) are accurate statements, but they proper nutrition. All of the options make reference to foods aren’t sufficiently related to the preceding statement. Option that most people view as healthful, but only option (B) (B) is a reasonable statement but has little to do with the discusses the nutritional value of foods. Therefore, the correct preceding statement. Only option (A) discusses the skills that answer is (B). Presidents need to lead their nations through difficult periods. Therefore, (A) is the correct answer.

Sample Question 30: Choose the opening sentence that goes best with the details in the paragraph. . New York surpassed Philadelphia not because of the superiority of its climate but because of the superiority of its harbor. It offered unimpeded access up the Hudson River. The city’s natural setting was a blessing occasionally mentioned in a patriotic address, though there was little knowledge of the natural processes that had led to the formation of the solid material on which the city’s streets were built. (A) Traces of the past in New York City are buried and hidden. (B) The geography of New York City was the city’s supreme advantage. (C) The reasons that the Dutch first came to New York City were largely commercial. (D) Most of New York City was covered by the great Laurentide glacier about 20,000 years ago.

Content Category: Supporting Details / Topic Sentences This question asks students to choose the best topic sentence for a paragraph on New York City’s natural resources in its early years. The best topic sentence will introduce the subject matter that is developed in the paragraph. Although each of the options discusses an aspect of New York City’s past, only option (B) discusses the advantageousness of New York City’s geography, the main subject of the paragraph. The correct answer, then, is (B).

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QUANTITATIVE REASONING Sample Question 34: If a ∆ b = a(a – b) and a b = b(b + a), what is the value of (8 ∆ 5) + (8 5)? (A) 21 (B) 29 Sample Question 32: Choose: (C) 89 (A) if the quantity in Column A is greater, (D) 128 (B) if the quantity in Column B is greater, (C) if the two quantities are equal, Content Category: Analysis (D) if not enough information is given for you to decide. This question introduces two newly defined operations, ∆ and Students are not expected to have seen these operations before, since the operations were made up for this question. Column A Column B Since a ∆ b = a(a – b), 8 ∆ 5 = 8(8 – 5) = 8 x 3 = 24 Since a b= b(b+ a), 8 5 = 5(5 + 8) = 5 x 13 = 65 p is an integer and 7 x p is even. The sum is 24 + 65, which equals 89. The correct answer is choice (C). The remainder whenp is 1 divided by 2.

Content Category: Extensions and Generalizations It is given that 7 × p is even, which means that it has 2 as one of its factors. The factor 2 is not in the 7 (since 7 is odd), so it must be in the integer p. This means thatp is even. Therefore, whenp is divided by 2, the remainder is 0. Since 0 is less than 1, the amount in column B is greater than the amount in column A. The correct answer is choice (B).

Sample Question 33: Choose: (A) if the quantity in Column A is greater, (B) if the quantity in Column B is greater, (C) if the two quantities are equal, (D) if not enough information is given for you to decide.

Column A Column B

A car traveled m miles. The average speed of the car, in miles per hour, was x; and the average speed of the car, in miles per minute, was y.

x y

Content Category: Analysis The car’s average speed is given asx miles per hour or y miles per minute. Since 1 hour = 60 minutes, a speed of x miles per hour is equivalent to x miles x or miles per minute. 60 minutes 60

Since the car’s average speed is y miles per minute, y = x /60. Since x > x /60, x must also be greater than y. Thus, the correct answer is choice (A). It is also possible to reason that the correct answer must be (A) because a car would go farther in 1 hour than it would go in 1 minute.

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MATHEMATICS

Sample Question 35: It takes light 0.000000001 second to travel 30 centimeters. What is this number of seconds written in scientific notation? (A) 1.0 x 109 (B) 1.0 x 108 -8 (C) 1.0 x 10 Sample Question 38: In triangle ABC, the ratio of x to y is -9 (D)1.0 x 10 2 to 3. What is the value of x?

Content Categories: Numbers and Number Relationships / (A) 20 Procedural Knowledge The problem here is to transform the (B) 26 number 0.000000001 to a number in the form 1.0 x 10n, where n (C) 40 is an integer. The number 1.0 is 1,000,000,000 (or 109) times (D) 52 0.000000001. The 9 in 109 can be found by counting the number of decimal places to the right of the decimal point (the decimal Content Categories: Geometry / Problem Solving point needs to move 9 places to the right to come to the spot In triangle ABC, one angle measures 50°. Since the sum of the just to the right of the digit 1). This means that 0.000000001 three angle measures is 180°, it follows that x + y = 130. In x equals 1.0 ÷ 109, which is 1.0 x 10-9. The correct answer is addition, the ratio of x to y is 2 to 3. This means that /y = 2/3 and choice (D). therefore y = 3/2x. Substituting 3/2x for y in the first equation gives x + 3/2x = 130. From this you can see that 2x + 3x = 260, so 5x = 260, and therefore x = 260/5 = 52. The correct answer is choice (D). Sample Question 36: In 1972, a loaf of bread cost $0.89. In 2000, the same loaf of bread cost $2.69. The price of bread increased by about what percent? Sample Question 39: A fair coin is tossed 4 times. What is (A) 33% the probability that it will land heads up all 4 times? (B) 67% (C) 200% (A) 2 (D) 300% (B) 1 (C) 1/8 Content Categories: Numbers and Number Relationships / (D) 1/16 Procedural Knowledge The increase in price can be found by subtracting $0.89 from $2.69, which is $1.80. The percent Content Categories: Probability / Problem Solving increase in price is equal to the amount of increase divided by One way to solve this problem is to list all the possible the original price, or $1.80 divided by $0.89. Since $1.80 is outcomes of the four coin tosses. It is a good idea to list them in about twice $0.89, the percent increase in the price of bread is a systematic way. Here is one way to do that. about 200%. The correct answer is choice (C). HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH Sample Question 37: A flower bed contains 72 orange daylilies, 65 yellow roses, 55 yellow marigolds, and 120 green HHTT HTTT THTT TTTT ferns. What is the ratio of orange flowers to yellow flowers? There are 16 possible outcomes, all equally likely. Only 1 outcome has all heads; so the probability of all heads is 1/16. It (A) 3 to 5 is also possible to use the concept of multiplying probabilities (B) 3 to 8 of independent events. The probability of a coin landing heads (C) 3 to 10 up in 1 toss is ½. So, the probability of this event occurring 4 (D) 3 to 13 times is ½ • ½ • ½ • ½ = 1/16. The correct answer is choice (D).

Content Categories: Numbers and Number Relationships / Procedural Knowledge There are 72 orange flowers and 65 + 55 or 120 yellow flowers. The ratio of orange flowers to yellow flowers is 72 to 120. This ratio can be simplified by dividing both terms by the greatest common factor, 24. The ratio in simplified form is 3 to 5. The correct answer is choice (A).

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MATHEMATICS CONTINUED Sample Question 42: If m = 7(3 + 5)k and k is a positive integer, which of the following must be a factor of m? (A) 5 (B) 10 (C) 14 (D) 21

Content Categories: Pre-Algebra / Conceptual Understanding The problem gives thatm = 7(3 + 5)k, which equals 7 x 8 x k. Since k is a positive integer, m is a multiple of both 7 and 8, and also a multiple of any combination of factors of 7 and 8. The answer choice that must be a factor of m is 14, since 14 is the product of 7 and 2 (and 2 is a factor of 8). Alternatively, the product of 7 and 8 is 56 and m = 56k. 14 is the only choice given that is a factor of 56. Therefore, 14 must be a factor of m. The correct answer is choice (C).

Sample Question 40: The graph above shows the m relationship between some American and European shoe Sample Question 43: The formula for density is d = /v , sizes. Based on the graph, which of the following is the range of where m stands for mass in grams and v stands for volume in European sizes that would include the American size 9? cubic centimeters. If steel has a density of 7.82 g/cm3 , what is (A) 35 to 37 the mass of a rectangular steel beam measuring 30 centimeters (B) 38 to 40 wide, 20 centimeters high, and 6 meters long? (C) 41 to 43 (A) 460.36g (D) 44 to 46 (B) 28,152g (C) 46,035.81g Content Categories: Pre-Algebra / Problem Solving (D) 2,815,200g On the graph, American shoe sizes are given on the horizontal axis and European shoe sizes are given on the vertical axis. The Content Categories: Pre-Algebra / Problem Solving six points in the body of the graph give six correspondences The question gives a formula and asks for a particular value of between American and European sizes. For example, an m. In the formula, the unit for m is grams (g), the unit for v is American size of 4 corresponds to a European size of 35. The six cubic centimeters (cm3) and the unit for d is grams per cubic points appear to lie approximately on a line. Noticing this centimeter (g/cm 3). The density for steel is given as 7.82 g /cm3. pattern allows you to approximate other correspondences, by You can figure out the volume in cubic centimeters, since the filling in or extending the line. The line can be extended up and dimensions of the beam are 30 cm, 20 cm, and 6 meters. to the right, to see that an American size 9 appears to Converting meters to centimeters gives 6 meters = 6 x 100 cm, correspond to a European size of about 42. This lies in the which equals 600 cm. The volume is 30 x 20 x 600 cm3, which is range 41 to 43. The correct answer is choice (C). 360,000 cm3. Substituting 7.82 for d and 360,000 for v in the formula gives m 7.82 = 360,000 Sample Question 41: If a = b, what is the value of 3 + 5(a – b)? Solve for m by multiplying 7.82 by 360,000. Students would not have calculators for this question, so some may choose to (A) 0 estimate the product as 8 x 400,000, or 3,200,000. In this (B) 3 estimate both rounding steps involved rounding up, so the (C) 5 actual answer is less than 3,200,000. The most reasonable (D) 8 answer choice is 2,815,200 g. The correct answer is choice (D).

Content Categories: Pre-Algebra / Conceptual Understanding If a = b, then a – b = 0, and the expression 3 + 5(a – b) equals 3 + 5(0). Since 5(0) = 0, the expression equals 3 + 0, or 3. The correct answer is choice (B).

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MATHEMATICS Optional Constructed-Response Questions (CTP 4 Only)

Sample Question 44: Each of the teachers in Town School ordered the same total number of candy bars, but some teachers ordered the candy bars in packs of 9, some ordered packs of 4, and some ordered packs of 15. What is the smallest total number of candy bars that each teacher could have Sample Question 45: In the figure above∆ABC is inscribed in ordered? the circle, centered at O, and AB = BC = √2. Show how you arrived at your answer. What is the area of the shaded region? Show your work or explain your reasoning. Content Category: Math Communication The number of candy bars ordered by each teacher must be a Content Category: Math Communication multiple of 9, a multiple of 4, and a multiple of 15. So the The shaded region given is inside the half of the circle above problem comes down to finding the least common multiple of diameter AC and outside of isosceles right triangle ABC. Therefore, 9, 4, and 15. One approach is to factor each number into its the area of the shaded region is the difference between the area of prime factors. the semicircle and the area of triangle ABC. 9 = 3 x 3 The area of the semicircle is half the area of the circle. You need to 4 = 2 x 2 find the radius of the circle to find its area. The radius of the circle is 15 = 3 x 5 half of a diameter. AC is a diameter of the circle and also the Common multiples of these three numbers must have 3, 3, 2, 2, hypotenuse of the triangle ABC. Using the Pythagorean Theorem, 2 2 and 5 as factors. The least common multiple is 3 x 3 x 2 x 2 x 5, you can find that the square of the length ofAC is (√2 ) + (√2 ) or 4. which is 180. It is also acceptable to list multiples of 9, 4, and 15 Therefore, AC = 2 and the radius of the circle is 1. This implies that 2 and pick 180 as the least number common to all three lists. the area of the circle is π(1) or π. Therefore, the area of the semicircle is π /2. Students receive a score of 2 for the correct answer (180) with (√2 ) (√2 ) The area of triangleABC is ½ (AB)(BC) = = 1 mathematically accurate work/explanations. 2 π Students receive a score of 1 if: 1) they answer 180 with work Therefore, the area of the shaded region is /2 – 1. missing or incomplete or work that has multiple arithmetic Students receive full credit (a score of 2) for the correct answer with errors; 2) they have a correct process, but because of an sufficient work/explanations. Student receives partial credit (a arithmetic error the answer is incorrect; or 3) they found a score of 1) if: 1) the correct answer is given with insufficient work/ common multiple of 9, 4, and 15 with work shown, but it is not explanations; 2) the answer given is incorrect, but the correct the least common multiple. process is followed or explained; or 3) the student applies the Pythagorean Theorem correctly and determines the correct areas of the semicircle and ∆ABC but does not find the difference between the areas.

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ALGEBRA 1 Sample Question 48: If a and b are constants and (ax + b)(2x – 3) = 2x2 + 5x – 12 for all values of x, what is the value of a + b? (A) 3 Sample Question 46: The solution of which of the (B) 4 following inequalities is the set of all numbers that are more (C) 5 than 2 units from 6? (D) 6 (A) |x| – 2 > 6 (B) |x – 2| > 6 Content Category: Equations and Inequalities 2 (C) |x – 6| > 2 (ax + b)(2x – 3) = 2x + 5x – 12 for all values of x. The product of 2 (D) |x| – 6 > 2 the factors (ax + b) and (2x – 3) is 2ax + 2bx – 3ax – 3b or 2ax + (2b – 3a)x – 3b. If this is equal to another quadratic in x Content Category: Equations and Inequalities for all values of x, then the coefficients of like terms must be Each inequality given involves absolute value, which can be equal. Therefore, 2a = 2 and –3b = –12, which implies a = 1 and defined relative to the real number line as follows. For any real b = 4. Additionally, 2b – 3a = 2 • 4 – 3 • 1 = 8 – 3 = 5. numbers, a and b, |a – b| is the distance between a and b on Thus, a + b = 1 + 4 = 5. The correct answer is choice (C). the real number line. Therefore, all numbersx that are more than 2 units from 6 or have a distance between x and 6 that is greater than 2 satisfy the inequality |x – 6| > 2. The correct answer is choice (C). Sample Question 49: The line containing points (1, –4) and (4, –7) must also contain point (A) (10, –10) (B) (0, –1) Sample Question 47: If a and b are both positive and ax + (C) (–1, –2) c + bx – y = 0, then x = (D) (–5, 3) y - c y - c (A) (C) ab a + b Content Category: ables, Graphs and Algebraic Geometry Any point on the line must satisfy its equation. The two given y + c y + c (B) (D) points on the line can be used to find the slope of the line. a - b ab -4 - (-7) 3 Slope = m = = = –1 1 - 4 -3 Content Category: Equations and Inequalities In the form y = mx + b, the equation of the line is y = –x + b. This Combine like terms and solve for x in the following manner. implies –4 = –(1) + b or b = –3. Thus, the equation of the line is ax + c + bx – y = 0 y = –x – 3. Of the choices, only option (C) satisfies this equation, ax + bx + c – y = 0 since –2 = –(–1) – 3. The correct answer is choice (C). (a + b)x + (c – y) = 0 (a + b)x = –(c – y) x = –(c – y) = y – c This problem can also be solved by focusing on the slope of the a + b a + b line. As we saw above, the slope of the line is equal to -4 - (-7) = -1. The slope of a line remains constant, so you The correct answer is choice (C). 1 - 4 can determine which point is on the line by determining which produces a slope of –1 with one of the given points.

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ALGEBRA 1 CONTINUED

Sample Question 50: Together Charlie and Patty have 45 books. Patty has twice as many books as Charlie. Let c represent the number of books Charlie has and p the number of books Patty has. Which of the following systems of equations best expresses this information? (A) c + p= 45 { p= 2c (B) { c + p= 45 c = 2p (C) { c = 2p p = c + 45 (D) { p = 2c c = p + 45

Content Category: Situations Involving Variable Quantities Since Charlie and Patty have 45 books together, the sum of the number of books each has is 45. Charlie has c books and Patty has p books; thus, c + p = 45. Additionally, Patty has twice as many books as Charlie, which means if the number of books that Charlie has is multiplied by 2, then the result should be the number of books that Patty has. Therefore,p = 2c. Thus, the system of equations that represents the given information is

c + p = 45 { p = 2c The correct answer is choice (A).

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